New Ratio Estimators Using Correlation Coefficient

Size: px
Start display at page:

Download "New Ratio Estimators Using Correlation Coefficient"

Transcription

1 New atio Estimators Usig Correlatio Coefficiet Cem Kadilar ad Hula Cigi Hacettepe Uiversit, Departmet of tatistics, Betepe, 06800, Akara, Turke. s : kadilar@hacettepe.edu.tr ; hcigi@hacettepe.edu.tr Abstract : We opose a class of ratio estimators for the estimatio of populatio mea b adaptig the estimators i igh ad Tailor (003) to the estimators i Kadilar ad Cigi (004). We obtai mea square error (ME) equatios for all oposed estimators, ad fid theoretical coditios that make each oposed estimator more efficiet tha the traditioal estimators, ad similarl for compariso to the ratio estimator i igh ad Tailor (003), ad for those i Kadilar ad Cigi (004). I additio, these coditios are supported b a umerical eample. Ke words : atio estimator, auiliar variable, simple radom samplig, efficiec. 000 AM Classificatio : 6 D 05, 6 G 05

2 1. Itroductio The classical ratio estimator for the populatio mea of the stud variable defied b r X (1) is where ad are the sample meas of stud ad auiliar variables, respectivel, ad it is assumed that the populatio mea X of the auiliar variable is kow. The ME of this estimator is as follows: where ad f ME ( r ) ( + [ θ]) () f respectivel; N ; is the sample size; N is the umber of uits i the populatio; are the populatio variaces of auiliar ad stud variables, ad X C θ. Here C ad C are the populatio C coefficiets of variatio of auiliar ad stud variables, respectivel (Cochra, 1977, pages ). igh ad Tailor (003) suggested the followig ratio estimator: T ( X + ) (3) + where is the correlatio coefficiet betwee auiliar ad stud variables. The ME of this ratio estimator is as follows: f ME ( T ) ( + ω[ ω θ]) (4)

3 X where ω. X + where ad Kadilar ad Cigi (004) suggested the followig ratio estimators: KC ( X ) X + b 1 (5) + b( X ) [ X + β ( )] (6) + β ( ) KC ( X C + b( X ) KC3 + ) (7) + C ( X ) [ Xβ ( C + b KC 4 ) + ] (8) β ( ) + C ( X ) [ X C + β ( ) + b ] (9) C + β ( ) KC 5 β ( ) is the populatio coefficiet of the kurtosis of the auiliar variable s b is the regressio coefficiet. Here s is the sample variace of s auiliar variable ad s is the sample covariace betwee the stud ad auiliar variables. Kadilar ad Cigi (004) obtaied the ME equatio of these ratio estimators as follows: ME f ( ) [ + ( )] ; i 1,,..., 5 KC i KC i (10) 3

4 where KC X 1 ; KC ; X + β ( ) KC3 ; X + C KC 4 Xβ β ( ) ( ) + C ad KC5 C. XC + β ( ). uggested Estimators Adaptig the estimator give i (3) to the estimators give i (5)-(9), we develop ew ratio estimators usig the correlatio coefficiet as follows: ( X ) ( + + b 1 X ) (11) + + b( X ) ( XC + ) (1) C + ( X C + b( X ) + ) (13) + C ( X ) [ X β ( + + b ) 4 β ( ) + ] (14) ( X ) [ X + β ( ) + b ] (15) + β ( ) 5 We obtai the ME equatio for these oposed estimators as ME f ( ) [ + ( )] ; i 1,,..., 5 i i (16) 4

5 where 1 ; X + C ; XC + ; X + C ( ) ( ) + β 4 ad Xβ 5. (for details see Appedi) X + β ( ) 3. Efficiec Comparisos I this sectio, we tr to obtai the efficiec coditios for the oposed estimators b comparig the ME of the oposed estimators with the ME of the sample mea, traditioal ratio estimator ad the ratio estimators suggested b igh ad Tailor (003) ad Kadilar ad Cigi (004). It is well kow that uder simple radom samplig without replacemet (WO) the variace of the sample mea is V f. (17) ( ) We first compare the ME of the oposed estimators, give i (16), with the variace of the sample mea. We have the followig coditio: Let υ ( ) < V ( ) ; i 1,,..., 5 ME i. i < 0, > υ i (18) Whe this coditio is satisfied, oposed estimators are more efficiet tha the sample mea. 5

6 ecodl, we compare the ME of the oposed estimators with the ME of the classical ratio estimator, give i (). We have the followig coditio: ME i ( ) < ME( ) ; i 1,,..., 5 > υ i r. < ( + θ) θ, i. (19) Whe this coditio is satisfied, oposed estimators are more efficiet tha the traditioal ratio estimator. Thirdl, we compare the ME of the oposed estimators with the ME of the estimator i igh ad Tailor (003), give i (4). We have the followig coditio: ME i ( ) < ME( ) ; i 1,,..., 5 > υ i T < ω ( ω + ωθ) ωθ, i. (0) Whe this coditio is satisfied, oposed estimators are more efficiet tha the ratio estimator, suggested b igh ad Tailor (003). Fiall, we compare the ME of the oposed estimators with the ME of the estimators i Kadilar ad Cigi (004), give i (10). We have the followig coditio: ME ( ) < ME( ) ; i 1,,..., 5 i KC j ad j 1,,,5. < i KC j (1) Whe this coditio is satisfied, oposed estimators are more efficiet tha the ratio estimators, suggested b Kadilar ad Cigi (004). We ca eamie the 6

7 coditio (1) for each oposed estimator. For eample, whe we take i j 1, we obtai the coditio: X < X + X + ( + ) > 0 X As is positive i ratio estimatio we have the followig coditio: > X This coditio is alwas satisfied if the auiliar variable has positive data. I other words, first oposed estimator is more efficiet tha first ratio estimator i Kadilar ad Cigi (004) whe the data are positive. Detail comparisos for the other oposed estimators ca also be studied i the same wa. Note that the efficiec comparisos amog the oposed estimators also result the similar coditio with (1) as follows: i < ; i j 1,,...,5 j () Whe this coditio is satisfied, ith oposed estimator is more efficiet tha jth oposed estimator. 4. Numerical Eample I this sectio, we appl the traditioal ratio estimator, give i (1), the igh- Tailor ratio estimator, give i (3), Kadilar-Cigi ratio estimators, give i (5)-(9) ad oposed estimators, give i (11)-(15), to data whose statistics are give i Table 1. We assume to take the sample size 50 from N00 usig WO. The ME of these estimators are computed as give i (), (4), (10) ad (16) ad these estimators are compared to each other with respect to their ME values. 7

8 Table 1 Data tatistics N KC X 5 KC β ( ) 50 KC C 15 θ 6.75 KC C ω 0.97 KC From Table, we uderstad that the most efficiet estimator is fifth oposed estimator. Whe we eamie the coditios, determied i ectio 3, for this data set, we see that all of them are satisfied for fifth oposed estimator as follows: 0.81 ad υ the coditio (18) is satisfied ad υ( + θ) the coditio (19) is satisfied ad υ( ω + ωθ) the coditio (0) is satisfied. 5 < ; i 1,,...,5 KC i the coditio (1) is satisfied. 5 < ; j 1,,3,4 j the coditio () is satisfied. 8

9 Therefore, we suggest that we should appl fifth oposed estimator to this data set. It is worth poit out that the traditioal ratio estimator is more efficiet tha the ratio estimator, suggested b igh ad Tailor (003), for this data set. Table ME Values of atio Estimators Estimators ME Estimators ME Estimators ME KC r KC T KC KC KC Coclusio We develop some ratio estimators usig the correlatio coefficiet ad theoreticall show that the oposed estimators have a smaller ME tha the traditioal, the igh ad Tailor's (003) ad Kadilar ad Cigi's (004) ratio estimators i certai coditios. These theoretical coditios are also satisfied b the results of a umerical eample. I future work, we hope to adapt the ratio estimators, eseted here, to ratio estimators i stratified radom samplig as i Kadilar ad Cigi (003; 005). Appedi To the first degree of apoimatio, the ME of the third oposed estimator ca be foud usig the Talor series method defied b 9

10 ( ) δσ δ ME (A.1) where ( c, d ) h ( c d ) h, δ, c B,, X d B,, X Σ f (see Wolter, 003, pages 1-8). Here B ; h ( c d ) h (, ) 3, i (13) ad deotes the populatio covariace betwee stud ad auiliar variables. Accordig to this defiitio, we obtai δ for the third oposed estimator as [ 1 B] δ. 3 We obtai the ME equatio of the third oposed estimator usig (A.1) as follows: ME f ( ) ( B + + B + B ) f f f f ( + + ) ( + ) [ + ( )]

11 We would like to remark that the ME equatios of the other oposed estimators ca easil be obtaied i the same wa. efereces Cigi, H. (1994). amplig Theor. Hacettepe Uiversit Press. Cochra, W.G. (1977). amplig Techiques. Joh Wile ad os, New-ork. Kadilar, C. ad Cigi, H. (005). A New atio Estimator i tratified adom amplig. Commuicatios i tatistics: Theor ad Methods\QT{it}{,} 34, Kadilar, C. ad Cigi, H. (004). atio Estimators i imple adom amplig. Applied Mathematics ad Computatio, 151, Kadilar, C. ad Cigi, H. (003). atio Estimators i tratified adom amplig. Biometrical Joural, 45, igh, H. P. ad Tailor,. (003). Use of Kow Correlatio Coefficiet i Estimatig the Fiite Populatio Mea. tatistics i Trasitio, 6, Upadhaa, L. N. ad igh, H. P. (1999). Use of Trasformed Auiliar Variable i Estimatig the Fiite Populatio Mea. Biometrical Joural, 41, Wolter, K. M. (003). Itroductio to Variace Estimatio. iger-verlag. 11

A General Family of Estimators for Estimating Population Variance Using Known Value of Some Population Parameter(s)

A General Family of Estimators for Estimating Population Variance Using Known Value of Some Population Parameter(s) Rajesh Sigh, Pakaj Chauha, Nirmala Sawa School of Statistics, DAVV, Idore (M.P.), Idia Floreti Smaradache Uiversity of New Meico, USA A Geeral Family of Estimators for Estimatig Populatio Variace Usig

More information

Modified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis

Modified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis America Joural of Mathematics ad Statistics 01, (4): 95-100 DOI: 10.593/j.ajms.01004.05 Modified Ratio s Usig Kow Media ad Co-Efficet of Kurtosis J.Subramai *, G.Kumarapadiya Departmet of Statistics, Podicherry

More information

Estimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable

Estimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable Iteratioal Joural of Probability ad Statistics 01, 1(4: 111-118 DOI: 10.593/j.ijps.010104.04 Estimatio of Populatio Mea Usig Co-Efficiet of Variatio ad Media of a Auxiliary Variable J. Subramai *, G. Kumarapadiya

More information

A Family of Unbiased Estimators of Population Mean Using an Auxiliary Variable

A Family of Unbiased Estimators of Population Mean Using an Auxiliary Variable Advaces i Computatioal Scieces ad Techolog ISSN 0973-6107 Volume 10, Number 1 (017 pp. 19-137 Research Idia Publicatios http://www.ripublicatio.com A Famil of Ubiased Estimators of Populatio Mea Usig a

More information

Abstract. Ranked set sampling, auxiliary variable, variance.

Abstract. Ranked set sampling, auxiliary variable, variance. Hacettepe Joural of Mathematics ad Statistics Volume (), 1 A class of Hartley-Ross type Ubiased estimators for Populatio Mea usig Raked Set Samplig Lakhkar Kha ad Javid Shabbir Abstract I this paper, we

More information

Enhancing ratio estimators for estimating population mean using maximum value of auxiliary variable

Enhancing ratio estimators for estimating population mean using maximum value of auxiliary variable J.Nat.Sci.Foudatio Sri Laka 08 46 (: 45-46 DOI: http://d.doi.org/0.408/jsfsr.v46i.8498 RESEARCH ARTICLE Ehacig ratio estimators for estimatig populatio mea usig maimum value of auiliar variable Nasir Abbas,

More information

Alternative Ratio Estimator of Population Mean in Simple Random Sampling

Alternative Ratio Estimator of Population Mean in Simple Random Sampling Joural of Mathematics Research; Vol. 6, No. 3; 014 ISSN 1916-9795 E-ISSN 1916-9809 Published by Caadia Ceter of Sciece ad Educatio Alterative Ratio Estimator of Populatio Mea i Simple Radom Samplig Ekaette

More information

Improved Ratio Estimators of Population Mean In Adaptive Cluster Sampling

Improved Ratio Estimators of Population Mean In Adaptive Cluster Sampling J. Stat. Appl. Pro. Lett. 3, o. 1, 1-6 (016) 1 Joural of Statistics Applicatios & Probability Letters A Iteratioal Joural http://dx.doi.org/10.18576/jsapl/030101 Improved Ratio Estimators of Populatio

More information

Improved exponential estimator for population variance using two auxiliary variables

Improved exponential estimator for population variance using two auxiliary variables OCTOGON MATHEMATICAL MAGAZINE Vol. 7, No., October 009, pp 667-67 ISSN -5657, ISBN 97-973-55-5-0, www.hetfalu.ro/octogo 667 Improved expoetial estimator for populatio variace usig two auxiliar variables

More information

Jambulingam Subramani 1, Gnanasegaran Kumarapandiyan 2 and Saminathan Balamurali 3

Jambulingam Subramani 1, Gnanasegaran Kumarapandiyan 2 and Saminathan Balamurali 3 ISSN 1684-8403 Joural of Statistics Volume, 015. pp. 84-305 Abstract A Class of Modified Liear Regressio Type Ratio Estimators for Estimatio of Populatio Mea usig Coefficiet of Variatio ad Quartiles of

More information

A Generalized Class of Estimators for Finite Population Variance in Presence of Measurement Errors

A Generalized Class of Estimators for Finite Population Variance in Presence of Measurement Errors Joural of Moder Applied Statistical Methods Volume Issue Article 3 --03 A Geeralized Class of Estimators for Fiite Populatio Variace i Presece of Measuremet Errors Praas Sharma Baaras Hidu Uiversit, Varaasi,

More information

Method of Estimation in the Presence of Nonresponse and Measurement Errors Simultaneously

Method of Estimation in the Presence of Nonresponse and Measurement Errors Simultaneously Joural of Moder Applied Statistical Methods Volume 4 Issue Article 5--05 Method of Estimatio i the Presece of Norespose ad Measuremet Errors Simultaeousl Rajesh Sigh Sigh Baaras Hidu Uiversit, Varaasi,

More information

Improvement in Estimating The Population Mean Using Dual To Ratio-Cum-Product Estimator in Simple Random Sampling

Improvement in Estimating The Population Mean Using Dual To Ratio-Cum-Product Estimator in Simple Random Sampling Olufadi Yuusa Departmet of tatistics ad Mathematical cieces Kwara tate Uiversit.M.B 53 Malete Nigeria ajesh igh Departmet of tatistics Baaras Hidu Uiversit Varaasi (U..) Idia Floreti maradache Uiversit

More information

Improved Class of Ratio -Cum- Product Estimators of Finite Population Mean in two Phase Sampling

Improved Class of Ratio -Cum- Product Estimators of Finite Population Mean in two Phase Sampling Global Joural of Sciece Frotier Research: F Mathematics ad Decisio Scieces Volume 4 Issue 2 Versio.0 Year 204 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic. (USA

More information

Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation

Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation Ope Joural o Statistics, 05, 5, -9 Published Olie Februar 05 i SciRes. http://www.scirp.org/joural/ojs http://dx.doi.org/0.436/ojs.05.500 Estimatio o Populatio Ratio i Post-Stratiied Samplig Usig Variable

More information

AClassofRegressionEstimatorwithCumDualProductEstimatorAsIntercept

AClassofRegressionEstimatorwithCumDualProductEstimatorAsIntercept Global Joural of Sciece Frotier Research: F Mathematics ad Decisio Scieces Volume 15 Issue 3 Versio 1.0 Year 2015 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic.

More information

Random Variables, Sampling and Estimation

Random Variables, Sampling and Estimation Chapter 1 Radom Variables, Samplig ad Estimatio 1.1 Itroductio This chapter will cover the most importat basic statistical theory you eed i order to uderstad the ecoometric material that will be comig

More information

A New Mixed Randomized Response Model

A New Mixed Randomized Response Model Iteratioal Joural of Busiess ad Social Sciece ol No ; October 00 A New Mixed adomized espose Model Aesha Nazuk NUST Busiess School Islamabad, Paksta E-mail: Aeshaazuk@bsedupk Phoe: 009-5-9085-367 Abstract

More information

Varanasi , India. Corresponding author

Varanasi , India. Corresponding author A Geeral Family of Estimators for Estimatig Populatio Mea i Systematic Samplig Usig Auxiliary Iformatio i the Presece of Missig Observatios Maoj K. Chaudhary, Sachi Malik, Jayat Sigh ad Rajesh Sigh Departmet

More information

A Family of Efficient Estimator in Circular Systematic Sampling

A Family of Efficient Estimator in Circular Systematic Sampling olumbia Iteratioal Publishig Joural of dvaced omputig (0) Vol. o. pp. 6-68 doi:0.776/jac.0.00 Research rticle Famil of Efficiet Estimator i ircular Sstematic Samplig Hemat K. Verma ad Rajesh Sigh * Received

More information

Research Article An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys

Research Article An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys Iteratioal Scholarly Research Network ISRN Probability ad Statistics Volume 01, Article ID 65768, 1 pages doi:10.50/01/65768 Research Article A Alterative Estimator for Estimatig the Fiite Populatio Mea

More information

REVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 1, 49-57, 2014

REVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 1, 49-57, 2014 EVISTA IVESTIGAIO OPEAIOAL VOL. 35, O., 9-57, 0 O A IMPOVED ATIO TYPE ESTIMATO OF FIITE POPULATIO MEA I SAMPLE SUVEYS A K P Swai Former Professor of Statistics, Utkal Uiversit, Bhubaeswar-7500, Idia ABSTAT

More information

Use of Auxiliary Information for Estimating Population Mean in Systematic Sampling under Non- Response

Use of Auxiliary Information for Estimating Population Mean in Systematic Sampling under Non- Response Maoj K. haudhar, Sachi Malik, Rajesh Sigh Departmet of Statistics, Baaras Hidu Uiversit Varaasi-005, Idia Floreti Smaradache Uiversit of New Mexico, Gallup, USA Use of Auxiliar Iformatio for Estimatig

More information

Some Exponential Ratio-Product Type Estimators using information on Auxiliary Attributes under Second Order Approximation

Some Exponential Ratio-Product Type Estimators using information on Auxiliary Attributes under Second Order Approximation ; [Formerly kow as the Bulleti of Statistics & Ecoomics (ISSN 097-70)]; ISSN 0975-556X; Year: 0, Volume:, Issue Number: ; It. j. stat. eco.; opyright 0 by ESER Publicatios Some Expoetial Ratio-Product

More information

Chain ratio-to-regression estimators in two-phase sampling in the presence of non-response

Chain ratio-to-regression estimators in two-phase sampling in the presence of non-response ProbStat Forum, Volume 08, July 015, Pages 95 10 ISS 0974-335 ProbStat Forum is a e-joural. For details please visit www.probstat.org.i Chai ratio-to-regressio estimators i two-phase samplig i the presece

More information

1 Inferential Methods for Correlation and Regression Analysis

1 Inferential Methods for Correlation and Regression Analysis 1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet

More information

Estimation of the Population Mean in Presence of Non-Response

Estimation of the Population Mean in Presence of Non-Response Commuicatios of the Korea Statistical Society 0, Vol. 8, No. 4, 537 548 DOI: 0.535/CKSS.0.8.4.537 Estimatio of the Populatio Mea i Presece of No-Respose Suil Kumar,a, Sadeep Bhougal b a Departmet of Statistics,

More information

Chapter 13, Part A Analysis of Variance and Experimental Design

Chapter 13, Part A Analysis of Variance and Experimental Design Slides Prepared by JOHN S. LOUCKS St. Edward s Uiversity Slide 1 Chapter 13, Part A Aalysis of Variace ad Eperimetal Desig Itroductio to Aalysis of Variace Aalysis of Variace: Testig for the Equality of

More information

Goodness-Of-Fit For The Generalized Exponential Distribution. Abstract

Goodness-Of-Fit For The Generalized Exponential Distribution. Abstract Goodess-Of-Fit For The Geeralized Expoetial Distributio By Amal S. Hassa stitute of Statistical Studies & Research Cairo Uiversity Abstract Recetly a ew distributio called geeralized expoetial or expoetiated

More information

Estimation of Gumbel Parameters under Ranked Set Sampling

Estimation of Gumbel Parameters under Ranked Set Sampling Joural of Moder Applied Statistical Methods Volume 13 Issue 2 Article 11-2014 Estimatio of Gumbel Parameters uder Raked Set Samplig Omar M. Yousef Al Balqa' Applied Uiversity, Zarqa, Jorda, abuyaza_o@yahoo.com

More information

Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters

Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters evista Colombiaa de Estadística Jauary 016, Volume 39, Issue 1, pp. 63 to 79 DOI: http://dx.doi.org/10.15446/rce.v391.55139 Ehacig the Mea atio Estimators for Estimatig Populatio Mea Usig No-Covetioal

More information

Properties and Hypothesis Testing

Properties and Hypothesis Testing Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.

More information

Investigating the Significance of a Correlation Coefficient using Jackknife Estimates

Investigating the Significance of a Correlation Coefficient using Jackknife Estimates Iteratioal Joural of Scieces: Basic ad Applied Research (IJSBAR) ISSN 2307-4531 (Prit & Olie) http://gssrr.org/idex.php?joural=jouralofbasicadapplied ---------------------------------------------------------------------------------------------------------------------------

More information

G. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan

G. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan Deviatio of the Variaces of Classical Estimators ad Negative Iteger Momet Estimator from Miimum Variace Boud with Referece to Maxwell Distributio G. R. Pasha Departmet of Statistics Bahauddi Zakariya Uiversity

More information

Research Article A Two-Parameter Ratio-Product-Ratio Estimator Using Auxiliary Information

Research Article A Two-Parameter Ratio-Product-Ratio Estimator Using Auxiliary Information Iteratioal Scholarly Research Network ISRN Probability ad Statistics Volume, Article ID 386, 5 pages doi:.54//386 Research Article A Two-Parameter Ratio-Product-Ratio Estimator Usig Auxiliary Iformatio

More information

On stratified randomized response sampling

On stratified randomized response sampling Model Assisted Statistics ad Applicatios 1 (005,006) 31 36 31 IOS ress O stratified radomized respose samplig Jea-Bok Ryu a,, Jog-Mi Kim b, Tae-Youg Heo c ad Chu Gu ark d a Statistics, Divisio of Life

More information

It should be unbiased, or approximately unbiased. Variance of the variance estimator should be small. That is, the variance estimator is stable.

It should be unbiased, or approximately unbiased. Variance of the variance estimator should be small. That is, the variance estimator is stable. Chapter 10 Variace Estimatio 10.1 Itroductio Variace estimatio is a importat practical problem i survey samplig. Variace estimates are used i two purposes. Oe is the aalytic purpose such as costructig

More information

SYSTEMATIC SAMPLING FOR NON-LINEAR TREND IN MILK YIELD DATA

SYSTEMATIC SAMPLING FOR NON-LINEAR TREND IN MILK YIELD DATA Joural of Reliability ad Statistical Studies; ISS (Prit): 0974-804, (Olie):9-5666 Vol. 7, Issue (04): 57-68 SYSTEMATIC SAMPLIG FOR O-LIEAR TRED I MILK YIELD DATA Tauj Kumar Padey ad Viod Kumar Departmet

More information

Goodness-Of-Fit For The Generalized Exponential Distribution. Abstract

Goodness-Of-Fit For The Generalized Exponential Distribution. Abstract Goodess-Of-Fit For The Geeralized Expoetial Distributio By Amal S. Hassa stitute of Statistical Studies & Research Cairo Uiversity Abstract Recetly a ew distributio called geeralized expoetial or expoetiated

More information

Topic 9: Sampling Distributions of Estimators

Topic 9: Sampling Distributions of Estimators Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be

More information

Confidence Interval for Standard Deviation of Normal Distribution with Known Coefficients of Variation

Confidence Interval for Standard Deviation of Normal Distribution with Known Coefficients of Variation Cofidece Iterval for tadard Deviatio of Normal Distributio with Kow Coefficiets of Variatio uparat Niwitpog Departmet of Applied tatistics, Faculty of Applied ciece Kig Mogkut s Uiversity of Techology

More information

The Random Walk For Dummies

The Random Walk For Dummies The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli

More information

Topic 9: Sampling Distributions of Estimators

Topic 9: Sampling Distributions of Estimators Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be

More information

Element sampling: Part 2

Element sampling: Part 2 Chapter 4 Elemet samplig: Part 2 4.1 Itroductio We ow cosider uequal probability samplig desigs which is very popular i practice. I the uequal probability samplig, we ca improve the efficiecy of the resultig

More information

SOME DOUBLE BINOMIAL SUMS RELATED WITH THE FIBONACCI, PELL AND GENERALIZED ORDER-k FIBONACCI NUMBERS

SOME DOUBLE BINOMIAL SUMS RELATED WITH THE FIBONACCI, PELL AND GENERALIZED ORDER-k FIBONACCI NUMBERS ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 43 Number 3 013 SOME DOUBLE BINOMIAL SUMS RELATED WITH THE FIBONACCI PELL AND GENERALIZED ORDER-k FIBONACCI NUMBERS EMRAH KILIÇ AND HELMUT PRODINGER ABSTRACT

More information

ON POINTWISE BINOMIAL APPROXIMATION

ON POINTWISE BINOMIAL APPROXIMATION Iteratioal Joural of Pure ad Applied Mathematics Volume 71 No. 1 2011, 57-66 ON POINTWISE BINOMIAL APPROXIMATION BY w-functions K. Teerapabolar 1, P. Wogkasem 2 Departmet of Mathematics Faculty of Sciece

More information

Sampling Error. Chapter 6 Student Lecture Notes 6-1. Business Statistics: A Decision-Making Approach, 6e. Chapter Goals

Sampling Error. Chapter 6 Student Lecture Notes 6-1. Business Statistics: A Decision-Making Approach, 6e. Chapter Goals Chapter 6 Studet Lecture Notes 6-1 Busiess Statistics: A Decisio-Makig Approach 6 th Editio Chapter 6 Itroductio to Samplig Distributios Chap 6-1 Chapter Goals After completig this chapter, you should

More information

CHAPTER 4 BIVARIATE DISTRIBUTION EXTENSION

CHAPTER 4 BIVARIATE DISTRIBUTION EXTENSION CHAPTER 4 BIVARIATE DISTRIBUTION EXTENSION 4. Itroductio Numerous bivariate discrete distributios have bee defied ad studied (see Mardia, 97 ad Kocherlakota ad Kocherlakota, 99) based o various methods

More information

Pattern Classification

Pattern Classification Patter Classificatio All materials i these slides were tae from Patter Classificatio (d ed) by R. O. Duda, P. E. Hart ad D. G. Stor, Joh Wiley & Sos, 000 with the permissio of the authors ad the publisher

More information

Journal of Scientific Research Vol. 62, 2018 : Banaras Hindu University, Varanasi ISSN :

Journal of Scientific Research Vol. 62, 2018 : Banaras Hindu University, Varanasi ISSN : Joural of Scietific Research Vol. 6 8 : 3-34 Baaras Hidu Uiversity Varaasi ISS : 447-9483 Geeralized ad trasformed two phase samplig Ratio ad Product ype stimators for Populatio Mea Usig uiliary haracter

More information

JOURNAL OF THE INDIAN SOCIETY OF AGRICULTURAL STATISTICS

JOURNAL OF THE INDIAN SOCIETY OF AGRICULTURAL STATISTICS Available olie at www.ia.org.i/jia JOURA OF THE IDIA OIETY OF AGRIUTURA TATITI 64() 00 55-60 Variace Etimatio for te Regreio Etimator of te Mea i tratified amplig UMMARY at Gupta * ad Javid abbir Departmet

More information

Developing Efficient Ratio and Product Type Exponential Estimators of Population Mean under Two Phase Sampling for Stratification

Developing Efficient Ratio and Product Type Exponential Estimators of Population Mean under Two Phase Sampling for Stratification America Joural of Operatioal Researc 05 5: -8 DOI: 0.593/j.ajor.05050.0 Developig Efficiet Ratio ad Product Type Epoetial Eimators of Populatio Mea uder Two Pase Samplig for Stratificatio Subas Kumar adav

More information

Pattern Classification

Pattern Classification Patter Classificatio All materials i these slides were tae from Patter Classificatio (d ed) by R. O. Duda, P. E. Hart ad D. G. Stor, Joh Wiley & Sos, 000 with the permissio of the authors ad the publisher

More information

Linear Regression Models

Linear Regression Models Liear Regressio Models Dr. Joh Mellor-Crummey Departmet of Computer Sciece Rice Uiversity johmc@cs.rice.edu COMP 528 Lecture 9 15 February 2005 Goals for Today Uderstad how to Use scatter diagrams to ispect

More information

Orthogonal Gaussian Filters for Signal Processing

Orthogonal Gaussian Filters for Signal Processing Orthogoal Gaussia Filters for Sigal Processig Mark Mackezie ad Kiet Tieu Mechaical Egieerig Uiversity of Wollogog.S.W. Australia Abstract A Gaussia filter usig the Hermite orthoormal series of fuctios

More information

Worksheet 23 ( ) Introduction to Simple Linear Regression (continued)

Worksheet 23 ( ) Introduction to Simple Linear Regression (continued) Worksheet 3 ( 11.5-11.8) Itroductio to Simple Liear Regressio (cotiued) This worksheet is a cotiuatio of Discussio Sheet 3; please complete that discussio sheet first if you have ot already doe so. This

More information

January 25, 2017 INTRODUCTION TO MATHEMATICAL STATISTICS

January 25, 2017 INTRODUCTION TO MATHEMATICAL STATISTICS Jauary 25, 207 INTRODUCTION TO MATHEMATICAL STATISTICS Abstract. A basic itroductio to statistics assumig kowledge of probability theory.. Probability I a typical udergraduate problem i probability, we

More information

INFINITE SEQUENCES AND SERIES

INFINITE SEQUENCES AND SERIES 11 INFINITE SEQUENCES AND SERIES INFINITE SEQUENCES AND SERIES 11.4 The Compariso Tests I this sectio, we will lear: How to fid the value of a series by comparig it with a kow series. COMPARISON TESTS

More information

SIMPLE LINEAR REGRESSION AND CORRELATION ANALYSIS

SIMPLE LINEAR REGRESSION AND CORRELATION ANALYSIS SIMPLE LINEAR REGRESSION AND CORRELATION ANALSIS INTRODUCTION There are lot of statistical ivestigatio to kow whether there is a relatioship amog variables Two aalyses: (1) regressio aalysis; () correlatio

More information

Bayesian and E- Bayesian Method of Estimation of Parameter of Rayleigh Distribution- A Bayesian Approach under Linex Loss Function

Bayesian and E- Bayesian Method of Estimation of Parameter of Rayleigh Distribution- A Bayesian Approach under Linex Loss Function Iteratioal Joural of Statistics ad Systems ISSN 973-2675 Volume 12, Number 4 (217), pp. 791-796 Research Idia Publicatios http://www.ripublicatio.com Bayesia ad E- Bayesia Method of Estimatio of Parameter

More information

An Improved Warner s Randomized Response Model

An Improved Warner s Randomized Response Model Iteratioal Joural of Statistics ad Applicatios 05, 5(6: 63-67 DOI: 0.593/j.statistics.050506.0 A Improved Warer s Radomized Respose Model F. B. Adebola, O. O. Johso * Departmet of Statistics, Federal Uiversit

More information

ANOTHER WEIGHTED WEIBULL DISTRIBUTION FROM AZZALINI S FAMILY

ANOTHER WEIGHTED WEIBULL DISTRIBUTION FROM AZZALINI S FAMILY ANOTHER WEIGHTED WEIBULL DISTRIBUTION FROM AZZALINI S FAMILY Sulema Nasiru, MSc. Departmet of Statistics, Faculty of Mathematical Scieces, Uiversity for Developmet Studies, Navrogo, Upper East Regio, Ghaa,

More information

Dual to Ratio Estimators for Mean Estimation in Successive Sampling using Auxiliary Information on Two Occasion

Dual to Ratio Estimators for Mean Estimation in Successive Sampling using Auxiliary Information on Two Occasion J. Stat. Appl. Pro. 7, o. 1, 49-58 (018) 49 Joural of Statistics Applicatios & Probability A Iteratioal Joural http://dx.doi.org/10.18576/jsap/070105 Dual to Ratio Estimators for Mea Estimatio i Successive

More information

7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals

7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals 7-1 Chapter 4 Part I. Samplig Distributios ad Cofidece Itervals 1 7- Sectio 1. Samplig Distributio 7-3 Usig Statistics Statistical Iferece: Predict ad forecast values of populatio parameters... Test hypotheses

More information

Chapter 8: Estimating with Confidence

Chapter 8: Estimating with Confidence Chapter 8: Estimatig with Cofidece Sectio 8.2 The Practice of Statistics, 4 th editio For AP* STARNES, YATES, MOORE Chapter 8 Estimatig with Cofidece 8.1 Cofidece Itervals: The Basics 8.2 8.3 Estimatig

More information

Topic 9: Sampling Distributions of Estimators

Topic 9: Sampling Distributions of Estimators Topic 9: Samplig Distributios of Estimators Course 003, 2016 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be

More information

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series

More information

(7 One- and Two-Sample Estimation Problem )

(7 One- and Two-Sample Estimation Problem ) 34 Stat Lecture Notes (7 Oe- ad Two-Sample Estimatio Problem ) ( Book*: Chapter 8,pg65) Probability& Statistics for Egieers & Scietists By Walpole, Myers, Myers, Ye Estimatio 1 ) ( ˆ S P i i Poit estimate:

More information

f(x i ; ) L(x; p) = i=1 To estimate the value of that maximizes L or equivalently ln L we will set =0, for i =1, 2,...,m p x i (1 p) 1 x i i=1

f(x i ; ) L(x; p) = i=1 To estimate the value of that maximizes L or equivalently ln L we will set =0, for i =1, 2,...,m p x i (1 p) 1 x i i=1 Parameter Estimatio Samples from a probability distributio F () are: [,,..., ] T.Theprobabilitydistributio has a parameter vector [,,..., m ] T. Estimator: Statistic used to estimate ukow. Estimate: Observed

More information

In this section we derive some finite-sample properties of the OLS estimator. b is an estimator of β. It is a function of the random sample data.

In this section we derive some finite-sample properties of the OLS estimator. b is an estimator of β. It is a function of the random sample data. 17 3. OLS Part III I this sectio we derive some fiite-sample properties of the OLS estimator. 3.1 The Samplig Distributio of the OLS Estimator y = Xβ + ε ; ε ~ N[0, σ 2 I ] b = (X X) 1 X y = f(y) ε is

More information

Expectation and Variance of a random variable

Expectation and Variance of a random variable Chapter 11 Expectatio ad Variace of a radom variable The aim of this lecture is to defie ad itroduce mathematical Expectatio ad variace of a fuctio of discrete & cotiuous radom variables ad the distributio

More information

Estimation of Backward Perturbation Bounds For Linear Least Squares Problem

Estimation of Backward Perturbation Bounds For Linear Least Squares Problem dvaced Sciece ad Techology Letters Vol.53 (ITS 4), pp.47-476 http://dx.doi.org/.457/astl.4.53.96 Estimatio of Bacward Perturbatio Bouds For Liear Least Squares Problem Xixiu Li School of Natural Scieces,

More information

On ratio and product methods with certain known population parameters of auxiliary variable in sample surveys

On ratio and product methods with certain known population parameters of auxiliary variable in sample surveys Statistics & Operatios Research Trasactios SORT 34 July-December 010, 157-180 ISSN: 1696-81 www.idescat.cat/sort/ Statistics & Operatios Research c Istitut d Estadística de Cataluya Trasactios sort@idescat.cat

More information

A statistical method to determine sample size to estimate characteristic value of soil parameters

A statistical method to determine sample size to estimate characteristic value of soil parameters A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig

More information

Mathematical Notation Math Introduction to Applied Statistics

Mathematical Notation Math Introduction to Applied Statistics Mathematical Notatio Math 113 - Itroductio to Applied Statistics Name : Use Word or WordPerfect to recreate the followig documets. Each article is worth 10 poits ad ca be prited ad give to the istructor

More information

April 18, 2017 CONFIDENCE INTERVALS AND HYPOTHESIS TESTING, UNDERGRADUATE MATH 526 STYLE

April 18, 2017 CONFIDENCE INTERVALS AND HYPOTHESIS TESTING, UNDERGRADUATE MATH 526 STYLE April 18, 2017 CONFIDENCE INTERVALS AND HYPOTHESIS TESTING, UNDERGRADUATE MATH 526 STYLE TERRY SOO Abstract These otes are adapted from whe I taught Math 526 ad meat to give a quick itroductio to cofidece

More information

Final Examination Solutions 17/6/2010

Final Examination Solutions 17/6/2010 The Islamic Uiversity of Gaza Faculty of Commerce epartmet of Ecoomics ad Political Scieces A Itroductio to Statistics Course (ECOE 30) Sprig Semester 009-00 Fial Eamiatio Solutios 7/6/00 Name: I: Istructor:

More information

Discrete Orthogonal Moment Features Using Chebyshev Polynomials

Discrete Orthogonal Moment Features Using Chebyshev Polynomials Discrete Orthogoal Momet Features Usig Chebyshev Polyomials R. Mukuda, 1 S.H.Og ad P.A. Lee 3 1 Faculty of Iformatio Sciece ad Techology, Multimedia Uiversity 75450 Malacca, Malaysia. Istitute of Mathematical

More information

Approximating the ruin probability of finite-time surplus process with Adaptive Moving Total Exponential Least Square

Approximating the ruin probability of finite-time surplus process with Adaptive Moving Total Exponential Least Square WSEAS TRANSACTONS o BUSNESS ad ECONOMCS S. Khotama, S. Boothiem, W. Klogdee Approimatig the rui probability of fiite-time surplus process with Adaptive Movig Total Epoetial Least Square S. KHOTAMA, S.

More information

Stat 319 Theory of Statistics (2) Exercises

Stat 319 Theory of Statistics (2) Exercises Kig Saud Uiversity College of Sciece Statistics ad Operatios Research Departmet Stat 39 Theory of Statistics () Exercises Refereces:. Itroductio to Mathematical Statistics, Sixth Editio, by R. Hogg, J.

More information

11 Correlation and Regression

11 Correlation and Regression 11 Correlatio Regressio 11.1 Multivariate Data Ofte we look at data where several variables are recorded for the same idividuals or samplig uits. For example, at a coastal weather statio, we might record

More information

Joint Probability Distributions and Random Samples. Jointly Distributed Random Variables. Chapter { }

Joint Probability Distributions and Random Samples. Jointly Distributed Random Variables. Chapter { } UCLA STAT A Applied Probability & Statistics for Egieers Istructor: Ivo Diov, Asst. Prof. I Statistics ad Neurology Teachig Assistat: Neda Farziia, UCLA Statistics Uiversity of Califoria, Los Ageles, Sprig

More information

The Sampling Distribution of the Maximum. Likelihood Estimators for the Parameters of. Beta-Binomial Distribution

The Sampling Distribution of the Maximum. Likelihood Estimators for the Parameters of. Beta-Binomial Distribution Iteratioal Mathematical Forum, Vol. 8, 2013, o. 26, 1263-1277 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.12988/imf.2013.3475 The Samplig Distributio of the Maimum Likelihood Estimators for the Parameters

More information

Expected Number of Level Crossings of Legendre Polynomials

Expected Number of Level Crossings of Legendre Polynomials Expected Number of Level Crossigs of Legedre olomials ROUT, LMNAYAK, SMOHANTY, SATTANAIK,NC OJHA,DRKMISHRA Research Scholar, G DEARTMENT OF MATHAMATICS,COLLEGE OF ENGINEERING AND TECHNOLOGY,BHUBANESWAR,ODISHA

More information

5. Fractional Hot deck Imputation

5. Fractional Hot deck Imputation 5. Fractioal Hot deck Imputatio Itroductio Suppose that we are iterested i estimatig θ EY or eve θ 2 P ry < c where y fy x where x is always observed ad y is subject to missigess. Assume MAR i the sese

More information

Continuous Data that can take on any real number (time/length) based on sample data. Categorical data can only be named or categorised

Continuous Data that can take on any real number (time/length) based on sample data. Categorical data can only be named or categorised Questio 1. (Topics 1-3) A populatio cosists of all the members of a group about which you wat to draw a coclusio (Greek letters (μ, σ, Ν) are used) A sample is the portio of the populatio selected for

More information

Double Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution

Double Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution Iteratioal Mathematical Forum, Vol., 3, o. 3, 3-53 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.9/imf.3.335 Double Stage Shrikage Estimator of Two Parameters Geeralized Expoetial Distributio Alaa M.

More information

Chapter 13: Tests of Hypothesis Section 13.1 Introduction

Chapter 13: Tests of Hypothesis Section 13.1 Introduction Chapter 13: Tests of Hypothesis Sectio 13.1 Itroductio RECAP: Chapter 1 discussed the Likelihood Ratio Method as a geeral approach to fid good test procedures. Testig for the Normal Mea Example, discussed

More information

Dept. of maths, MJ College.

Dept. of maths, MJ College. 8. CORRELATION Defiitios: 1. Correlatio Aalsis attempts to determie the degree of relatioship betwee variables- Ya-Ku-Chou.. Correlatio is a aalsis of the covariatio betwee two or more variables.- A.M.Tuttle.

More information

MOMENT-METHOD ESTIMATION BASED ON CENSORED SAMPLE

MOMENT-METHOD ESTIMATION BASED ON CENSORED SAMPLE Vol. 8 o. Joural of Systems Sciece ad Complexity Apr., 5 MOMET-METHOD ESTIMATIO BASED O CESORED SAMPLE I Zhogxi Departmet of Mathematics, East Chia Uiversity of Sciece ad Techology, Shaghai 37, Chia. Email:

More information

Sample Size Determination (Two or More Samples)

Sample Size Determination (Two or More Samples) Sample Sie Determiatio (Two or More Samples) STATGRAPHICS Rev. 963 Summary... Data Iput... Aalysis Summary... 5 Power Curve... 5 Calculatios... 6 Summary This procedure determies a suitable sample sie

More information

Resampling Methods. X (1/2), i.e., Pr (X i m) = 1/2. We order the data: X (1) X (2) X (n). Define the sample median: ( n.

Resampling Methods. X (1/2), i.e., Pr (X i m) = 1/2. We order the data: X (1) X (2) X (n). Define the sample median: ( n. Jauary 1, 2019 Resamplig Methods Motivatio We have so may estimators with the property θ θ d N 0, σ 2 We ca also write θ a N θ, σ 2 /, where a meas approximately distributed as Oce we have a cosistet estimator

More information

Quick Review of Probability

Quick Review of Probability Quick Review of Probability Berli Che Departmet of Computer Sciece & Iformatio Egieerig Natioal Taiwa Normal Uiversity Refereces: 1. W. Navidi. Statistics for Egieerig ad Scietists. Chapter 2 & Teachig

More information

Quick Review of Probability

Quick Review of Probability Quick Review of Probability Berli Che Departmet of Computer Sciece & Iformatio Egieerig Natioal Taiwa Normal Uiversity Refereces: 1. W. Navidi. Statistics for Egieerig ad Scietists. Chapter & Teachig Material.

More information

Simple Random Sampling!

Simple Random Sampling! Simple Radom Samplig! Professor Ro Fricker! Naval Postgraduate School! Moterey, Califoria! Readig:! 3/26/13 Scheaffer et al. chapter 4! 1 Goals for this Lecture! Defie simple radom samplig (SRS) ad discuss

More information

First, note that the LS residuals are orthogonal to the regressors. X Xb X y = 0 ( normal equations ; (k 1) ) So,

First, note that the LS residuals are orthogonal to the regressors. X Xb X y = 0 ( normal equations ; (k 1) ) So, 0 2. OLS Part II The OLS residuals are orthogoal to the regressors. If the model icludes a itercept, the orthogoality of the residuals ad regressors gives rise to three results, which have limited practical

More information

A proposed discrete distribution for the statistical modeling of

A proposed discrete distribution for the statistical modeling of It. Statistical Ist.: Proc. 58th World Statistical Cogress, 0, Dubli (Sessio CPS047) p.5059 A proposed discrete distributio for the statistical modelig of Likert data Kidd, Marti Cetre for Statistical

More information

Chapter 10: Power Series

Chapter 10: Power Series Chapter : Power Series 57 Chapter Overview: Power Series The reaso series are part of a Calculus course is that there are fuctios which caot be itegrated. All power series, though, ca be itegrated because

More information

Stat 421-SP2012 Interval Estimation Section

Stat 421-SP2012 Interval Estimation Section Stat 41-SP01 Iterval Estimatio Sectio 11.1-11. We ow uderstad (Chapter 10) how to fid poit estimators of a ukow parameter. o However, a poit estimate does ot provide ay iformatio about the ucertaity (possible

More information

6.3 Testing Series With Positive Terms

6.3 Testing Series With Positive Terms 6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial

More information