Varanasi , India. Corresponding author


 Silas Parker
 2 years ago
 Views:
Transcription
1 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 of Statistics, Baaras Hidu Uiversity Varaasi005, Idia Departmet of Statistics, Rajastha Uiversity, Jaipur, Idia Correspodig author Abstract This paper proposes a geeral family of estimators for estimatig the populatio mea i systematic samplig i the presece of orespose adaptig the family of estimators proposed by Khoshevisa et al. (007). I this paper we have discussed the geeral properties of the proposed family icludig optimum property. The results have bee illustrated umerically by takig a empirical populatio cosidered i the literature. Keywords: Family of estimators, Auxiliary iformatio, Mea square error, Norespose, Systematic samplig.. Itroductio The method of systematic samplig, first studied by Madow ad Madow (944), is used widely i surveys of fiite populatios. Whe properly applied, the methods pocks up ay obvious or hidde stratificatio i the populatio ad thus ca be more precise tha radom samplig. I additio, systematic samplig is implemeted easily, thus reducig costs. I this variat of radom samplig, oly the first uit of the sample is selected at radom from the populatio. The subsequet uits are the selected by followig some defiite rule. Systematic samplig has bee cosidered i detail by Cochra (946) ad Lahiri (954). Reviews of the work doe i the field have bee give by ates (948) ad
2 Bucklad (95). The applicatio of systematic samplig to forest surveys has bee illustrated by Hasel (94), Fiey (948) ad Nair ad Bhargava (95). Use of systematic samplig i estimatig catch of fish has bee demostrated by Sukhatme et al. (958). The use of auxiliary iformatio has bee permeated the importat role to improve the efficiecy of the estimator. Kushwaha ad Sigh (989) suggested a class of almost ubiased ratio ad product type estimators for estimatig the populatio mea usig jackkife techique iitiated by Queouille (956). Afterward Baarasi et al. (993) ad Sigh ad Sigh (998) have proposed the estimators of populatio mea usig auxiliary iformatio i systematic samplig. Khoshevisa et al. (007) suggested a geeral family of estimators for estimatig the populatios mea usig kow values of some populatio parameters i simple radom samplig, give by a + b t = y (.) α(ax + b) + ( α)(a + b) where y ad x are the sample meas of study ad auxiliary variables respectively. is the populatio mea of auxiliary variable. a 0 ad b are either real umbers or fuctios of kow parameters of auxiliary variable. α ad g are the real umbers which are to be determied. Here we would like to metio that the choice of the estimator depeds o the availability ad values of the various parameter(s) used (for choice of the parameters a ad b refer to Sigh et al. (008) ad Sigh ad Kumar(0)). I this paper we have proposed a geeral family of estimators for estimatig the populatio mea i systematic samplig usig auxiliary iformatio i the presece of orespose followig Khoshevisa et al. (007). We have also derived the expressios for miimum mea square errors (MSE) of the family with respect to α. A comparative study is also carried out to compare the optimum estimators of the family with respect to usual mea estimator with the help of umerical data. g. Proposed Family of Estimators Let us suppose that a populatio cosists of N uits umbered from to N i some order ad a sample of size is to be draw such that N = k ( k is a iteger). Thus
3 there will be k samples each of uits ad we select oe sample from the set of k samples. Let ad be the study ad auxiliary variable with respective meas ad. Let us cosider yij(xij) be the th j observatio i the th i systematic sample uder study (auxiliary) variable ( i =...k : j =... ). Wwe assume that the orespose is observed oly o study variable ad auxiliary variable is free from orespose. Usig HaseHurwitz (946) techique of subsamplig of orespodets, the estimator of populatio mea, ca be defied as where y ad y y yh = (.) + y h are, respectively the meas based o respodet uits from the systematic sample of uits ad subsample of h uits selected from o respodet uits i the systematic sample. The estimator of populatio mea of auxiliary variable based o the systematic sample of size uits, is give by x ij j= x = ( i =... k ) (.) Obviously, y ad x are ubiased estimators. The variace expressio for the estimators ad ( x) where y ad x are, respectively, give by N V y = L { + ρ} S + WS V = { + ( ) ρ } S (.3) (.4) ρ ad ρ are the correlatio coefficiets betwee a pair of uits withi the systematic sample for the study ad auxiliary variables respectively. S ad respectively the mea squares of the etire group for study ad auxiliary variable. S are be the mea square of orespose group uder study variable, W is the orespose rate i the populatio ad L =. h S
4 Let us assume that the populatio mea is kow. Thus the usual ratio ad product estimators of the populatio mea uder orespose based o a systematic sample of size, ca be respectively defied as ad y y R = (.5) x y P = y x (.6) To obtai the biases ad mea square errors, we use large sample approximatio. y = ( + ) e 0 x = ( + ) e e such that E ( e 0 ) = ( ) ( ) E e 0 = ( ) e V y V( x) E = ad E ( e 0 e ) = where respectively. E = 0, ad L S = { + ρ } C + W, = { + } C, Cov y, x ρ = { + ρ } { + ρ} ρcc C ad C are the coefficiets of variatio of study ad auxiliary variables Expressig the equatios (.5) ad (.6) i terms of i expectatios the bias expressios of the estimators of by ad y R B = + y P { ρ}( Kρ ) C B = { + ρ} Kρ C e s ( 0,) i = ad takig y R ad y P, are respectively give (.7) (.8)
5 where, ρ = { + ρ} { + ρ } C ad K = ρ. C The mea square errors (MSE s) of y R N MSE = + ad P y MSE = + y R ad y P, are respectively, give by + ρ L C K C + W S { } ( ) ρ ρ N { } ( ) ρ ρ C + + Kρ C + L W S (.9) (.0) Motivated by Khoshevisa et al. (007), we ow defie a family of estimators of populatio mea based o a systematic sample of size i the presece of orespose as t g a + b = y (.) α( ax + b) + ( α)( a + b) This family ca geerate the orespose versios of a umber of estimators of populatio mea icludig the usual ratio ad product estimators o differet choices of a, b, α ad g.. Properties of Expressig t t a where λ =. a + b t i terms of e i s, we get ( + e )( + αλe ) g = y 0 (.) We assume that λ e < so that the right had side of the equatio (.) is expadable i terms of power series. Expadig the right had side of the equatio (.) ad eglectig the terms i e i s havig power greater tha two, we have
6 g(g + ) t = e0 gαλe + α λ e gαλe0e (.3) Takig expectatio both the sides of equatio (.3), we get the bias of t up to the first order of approximatio, as ( t ) B = { + ρ } ( g + ) N g C α λ gαλkρ (.4) Squarig both the sides of the equatio (.3) ad the takig the expectatio, we obtai the MSE of t up to the first order of approximatio, as ( t ) N MSE = +. Optimum Choice of α { } ( ) ρ ρ C + g α λ gαλρ K C I order to obtai the miimum MSE of respect to α ad equatig the derivative to zero, we get { + ρ }[ αg λ gλρ K] C L + ( ) t, we differetiate the MSE of The equatio (.6) provides the optimum values of α as W S (.5) t with = 0 (.6) ρ K α = gλ (.7) Puttig the optimum value of α from equatio (.7) ito the equatio (.5), we get the miimum MSE of t, as ( t ) mi MSE = + { ρ }[ C K C ] ρ L + ( ) W S (.8)
7 The miimum MSE of t, is same as the mea square error of the usual regressio estimator i systematic samplig uder orespose. 3. Empirical Study For umerical illustratio, we have cosidered the data give i Murthy (967, p. 33). The data are based o legth () ad timber volume () for 76 forest strips. Murthy (967, p.49) ad Kushwaha ad Sigh (989) reported the values of itraclass correlatio coefficiets ρ ad ρ approximately equal for the systematic sample of size 6 by eumeratig all possible systematic samples after arragig the data i ascedig order of strip legth. The details of populatio parameters are : N = 76, = 6, = 8.636, = , S = , S = , ρ = 0.870, 3 S = S 4 = Table shows the percetage relative efficiecy (PRE) of t (optimum) with respect to y for the differet choices of W ad L. Table : PRE of t (optimum) with respect to y W L PRE
8 Coclusio I this paper, we have proposed a geeral family of estimators of populatio mea i systematic samplig usig a auxiliary variable i the presece of orespose. The optimum property of the family has bee discussed. The study cocludes that the suggested family coverges to the usual regressio estimator of populatio mea i systematic samplig uder orespose if the parameter α attais its optimum value. From Table, it ca easily be see that the estimator t (optimum) performs always better tha the usual estimator y. It is also observed that the percetage relative efficiecy (PRE) of t (optimum) with respect to y decreases with icrease i orespose rate W as well as L. Refereces. Baarasi, Kushwaha, S.N.S. ad Kushwaha, K.S. (993): A class of ratio, product ad differece (RPD) estimators i systematic samplig, Microelectro. Reliab., 33, 4,
9 . Bucklad, W. R. (95): A review of the literature of systematic samplig, JRSS, (B), 3, Cochra, W. G. (946): Relative accuracy of systematic ad stratified radom samples for a certai class of populatio, AMS, 7, Fiey, D.J. (948): Radom ad systematic samplig i timber surveys, Forestry,, Hase, M. H. ad Hurwitz, W. N. (946) : The problem of orespose i sample surveys, Jour. of The Amer. Stat. Assoc., 4, Hasel, A. A. (94): Estimatio of volume i timber stads by strip samplig, AMS, 3, Khoshevisa, M., Sigh, R., Chauha, P., Sawa, N. ad Smaradache, F. (007): A geeral family of estimators for estimatig populatio mea usig kow value of some populatio parameter(s). Far East J. Theor. Statist.,, Kushwaha, K. S. ad Sigh, H.P. (989): Class of almost ubiased ratio ad product estimators i systematic samplig, Jour. Id. Soc. Ag. Statistics, 4,, Lahiri, D. B. (954): O the questio of bias of systematic samplig, Proceedigs of World Populatio Coferece, 6, Madow, W. G. ad Madow, L.H. (944): O the theory of systematic samplig, I. A. Math. Statist., 5, 4.. Murthy, M.N. (967): Samplig Theory ad Methods. Statistical Publishig Society, Calcutta.. Nair, K. R. ad Bhargava, R. P. (95): Statistical samplig i timber surveys i Idia, Forest Research Istitute, Dehradu, Idia forest leaflet, Queouille, M. H. (956): Notes o bias i estimatio, Biometrika, 43, Sigh, R ad Sigh, H. P. (998): Almost ubiased ratio ad product type estimators i systematic samplig, Questiio,,3, Sigh, R., Kumar, M. ad Smaradache, F. (008): Almost Ubiased Estimator for Estimatig Populatio Mea Usig Kow Value of Some Populatio Parameter(s). Pak. J. Stat. Oper. Res., 4() pp6376.
10 6. Sigh, R. ad Kumar, M. (0): A ote o trasformatios o auxiliary variable i survey samplig. MASA, 6:, Sukhatme, P. V., Paes, V. G. ad Sastry, K. V. R. (958): Samplig techiques for estimatig the catch of sea fish i Idia, Biometrics, 4, ates, F. (948): Systematic samplig, Philosophical Trasactios of Royal Society, (A), 4,
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 Varaasi005, Idia Floreti Smaradache Uiversit of New Mexico, Gallup, USA Use of Auxiliar Iformatio for Estimatig
More informationSome Exponential RatioProduct Type Estimators using information on Auxiliary Attributes under Second Order Approximation
; [Formerly kow as the Bulleti of Statistics & Ecoomics (ISSN 09770)]; ISSN 0975556X; Year: 0, Volume:, Issue Number: ; It. j. stat. eco.; opyright 0 by ESER Publicatios Some Expoetial RatioProduct
More informationA 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 informationImproved exponential estimator for population variance using two auxiliary variables
OCTOGON MATHEMATICAL MAGAZINE Vol. 7, No., October 009, pp 66767 ISSN 5657, ISBN 979735550, www.hetfalu.ro/octogo 667 Improved expoetial estimator for populatio variace usig two auxiliar variables
More informationImproved 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 informationChain ratiotoregression estimators in twophase sampling in the presence of nonresponse
ProbStat Forum, Volume 08, July 015, Pages 95 10 ISS 0974335 ProbStat Forum is a ejoural. For details please visit www.probstat.org.i Chai ratiotoregressio estimators i twophase samplig i the presece
More informationA Family of Unbiased Estimators of Population Mean Using an Auxiliary Variable
Advaces i Computatioal Scieces ad Techolog ISSN 09736107 Volume 10, Number 1 (017 pp. 19137 Research Idia Publicatios http://www.ripublicatio.com A Famil of Ubiased Estimators of Populatio Mea Usig a
More informationEstimation of the Population Mean in Presence of NonResponse
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 NoRespose Suil Kumar,a, Sadeep Bhougal b a Departmet of Statistics,
More informationA 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 informationJournal of Scientific Research Vol. 62, 2018 : Banaras Hindu University, Varanasi ISSN :
Joural of Scietific Research Vol. 6 8 : 334 Baaras Hidu Uiversity Varaasi ISS : 4479483 Geeralized ad trasformed two phase samplig Ratio ad Product ype stimators for Populatio Mea Usig uiliary haracter
More informationEstimation of Population Mean Using CoEfficient of Variation and Median of an Auxiliary Variable
Iteratioal Joural of Probability ad Statistics 01, 1(4: 111118 DOI: 10.593/j.ijps.010104.04 Estimatio of Populatio Mea Usig CoEfficiet of Variatio ad Media of a Auxiliary Variable J. Subramai *, G. Kumarapadiya
More informationModified Ratio Estimators Using Known Median and CoEfficent of Kurtosis
America Joural of Mathematics ad Statistics 01, (4): 95100 DOI: 10.593/j.ajms.01004.05 Modified Ratio s Usig Kow Media ad CoEfficet of Kurtosis J.Subramai *, G.Kumarapadiya Departmet of Statistics, Podicherry
More informationSYSTEMATIC SAMPLING FOR NONLINEAR TREND IN MILK YIELD DATA
Joural of Reliability ad Statistical Studies; ISS (Prit): 0974804, (Olie):95666 Vol. 7, Issue (04): 5768 SYSTEMATIC SAMPLIG FOR OLIEAR TRED I MILK YIELD DATA Tauj Kumar Padey ad Viod Kumar Departmet
More informationAClassofRegressionEstimatorwithCumDualProductEstimatorAsIntercept
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 informationMethod of Estimation in the Presence of Nonresponse and Measurement Errors Simultaneously
Joural of Moder Applied Statistical Methods Volume 4 Issue Article 505 Method of Estimatio i the Presece of Norespose ad Measuremet Errors Simultaeousl Rajesh Sigh Sigh Baaras Hidu Uiversit, Varaasi,
More informationImproved Ratio Estimators of Population Mean In Adaptive Cluster Sampling
J. Stat. Appl. Pro. Lett. 3, o. 1, 16 (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 informationResearch 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 informationRandom 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 informationAlternative Ratio Estimator of Population Mean in Simple Random Sampling
Joural of Mathematics Research; Vol. 6, No. 3; 014 ISSN 19169795 EISSN 19169809 Published by Caadia Ceter of Sciece ad Educatio Alterative Ratio Estimator of Populatio Mea i Simple Radom Samplig Ekaette
More informationA Family of Efficient Estimator in Circular Systematic Sampling
olumbia Iteratioal Publishig Joural of dvaced omputig (0) Vol. o. pp. 668 doi:0.776/jac.0.00 Research rticle Famil of Efficiet Estimator i ircular Sstematic Samplig Hemat K. Verma ad Rajesh Sigh * Received
More informationJambulingam Subramani 1, Gnanasegaran Kumarapandiyan 2 and Saminathan Balamurali 3
ISSN 16848403 Joural of Statistics Volume, 015. pp. 84305 Abstract A Class of Modified Liear Regressio Type Ratio Estimators for Estimatio of Populatio Mea usig Coefficiet of Variatio ad Quartiles of
More informationA Generalized Class of Unbiased Estimators for Population Mean Using Auxiliary Information on an Attribute and an Auxiliary Variable
Iteratioal Joural of Computatioal ad Applied Mathematics. ISSN 894966 Volume, Number 07, pp. 8 Research Idia ublicatios http://www.ripublicatio.com A Geeralized Class of Ubiased Estimators for opulatio
More informationAbstract. Ranked set sampling, auxiliary variable, variance.
Hacettepe Joural of Mathematics ad Statistics Volume (), 1 A class of HartleyRoss type Ubiased estimators for Populatio Mea usig Raked Set Samplig Lakhkar Kha ad Javid Shabbir Abstract I this paper, we
More informationOn ratio and product methods with certain known population parameters of auxiliary variable in sample surveys
Statistics & Operatios Research Trasactios SORT 34 JulyDecember 010, 157180 ISSN: 169681 www.idescat.cat/sort/ Statistics & Operatios Research c Istitut d Estadística de Cataluya Trasactios sort@idescat.cat
More informationChapter 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 informationProperties 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. Crosssectioal data. 2. Time series data.
More informationNew Ratio Estimators Using Correlation Coefficient
New atio Estimators Usig Correlatio Coefficiet Cem Kadilar ad Hula Cigi Hacettepe Uiversit, Departmet of tatistics, Betepe, 06800, Akara, Turke. emails : kadilar@hacettepe.edu.tr ; hcigi@hacettepe.edu.tr
More informationSimple 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 informationDual to Ratio Estimators for Mean Estimation in Successive Sampling using Auxiliary Information on Two Occasion
J. Stat. Appl. Pro. 7, o. 1, 4958 (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 informationDouble Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution
Iteratioal Mathematical Forum, Vol., 3, o. 3, 353 HIKARI Ltd, www.mhikari.com http://dx.doi.org/.9/imf.3.335 Double Stage Shrikage Estimator of Two Parameters Geeralized Expoetial Distributio Alaa M.
More informationEstimation of Population Mean in Presence of NonResponse in Double Sampling
J. Stat. Appl. Pro. 6, No. 2, 345353 (2017) 345 Joural of Statistics Applicatios & Probability A Iteratioal Joural http://dx.doi.org/10.18576/jsap/060209 Estimatio of Populatio Mea i Presece of NoRespose
More informationEstimation of Gumbel Parameters under Ranked Set Sampling
Joural of Moder Applied Statistical Methods Volume 13 Issue 2 Article 112014 Estimatio of Gumbel Parameters uder Raked Set Samplig Omar M. Yousef Al Balqa' Applied Uiversity, Zarqa, Jorda, abuyaza_o@yahoo.com
More informationEstimation of Population Ratio in PostStratified 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 PostStratiied Samplig Usig Variable
More informationOn stratified randomized response sampling
Model Assisted Statistics ad Applicatios 1 (005,006) 31 36 31 IOS ress O stratified radomized respose samplig JeaBok Ryu a,, JogMi Kim b, TaeYoug Heo c ad Chu Gu ark d a Statistics, Divisio of Life
More informationG. 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 informationElement 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 informationTopic 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 information5. 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 informationAn Improved Warner s Randomized Response Model
Iteratioal Joural of Statistics ad Applicatios 05, 5(6: 6367 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 informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals
More informationCSE 527, Additional notes on MLE & EM
CSE 57 Lecture Notes: MLE & EM CSE 57, Additioal otes o MLE & EM Based o earlier otes by C. Grat & M. Narasimha Itroductio Last lecture we bega a examiatio of model based clusterig. This lecture will be
More informationUnbiased Estimation. February 712, 2008
Ubiased Estimatio February 72, 2008 We begi with a sample X = (X,..., X ) of radom variables chose accordig to oe of a family of probabilities P θ where θ is elemet from the parameter space Θ. For radom
More informationThe Sampling Distribution of the Maximum. Likelihood Estimators for the Parameters of. BetaBinomial Distribution
Iteratioal Mathematical Forum, Vol. 8, 2013, o. 26, 12631277 HIKARI Ltd, www.mhikari.com http://d.doi.org/10.12988/imf.2013.3475 The Samplig Distributio of the Maimum Likelihood Estimators for the Parameters
More informationREVISTA INVESTIGACION OPERACIONAL VOL. 35, NO. 1, 4957, 2014
EVISTA IVESTIGAIO OPEAIOAL VOL. 35, O., 957, 0 O A IMPOVED ATIO TYPE ESTIMATO OF FIITE POPULATIO MEA I SAMPLE SUVEYS A K P Swai Former Professor of Statistics, Utkal Uiversit, Bhubaeswar7500, Idia ABSTAT
More informationON POINTWISE BINOMIAL APPROXIMATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 71 No. 1 2011, 5766 ON POINTWISE BINOMIAL APPROXIMATION BY wfunctions K. Teerapabolar 1, P. Wogkasem 2 Departmet of Mathematics Faculty of Sciece
More informationLecture 3. Properties of Summary Statistics: Sampling Distribution
Lecture 3 Properties of Summary Statistics: Samplig Distributio Mai Theme How ca we use math to justify that our umerical summaries from the sample are good summaries of the populatio? Lecture Summary
More informationA 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 informationActivity 3: Length Measurements with the FourSided Meter Stick
Activity 3: Legth Measuremets with the FourSided Meter Stick OBJECTIVE: The purpose of this experimet is to study errors ad the propagatio of errors whe experimetal data derived usig a foursided meter
More informationMATH 320: Probability and Statistics 9. Estimation and Testing of Parameters. Readings: Pruim, Chapter 4
MATH 30: Probability ad Statistics 9. Estimatio ad Testig of Parameters Estimatio ad Testig of Parameters We have bee dealig situatios i which we have full kowledge of the distributio of a radom variable.
More informationConfidence 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 informationMath 155 (Lecture 3)
Math 55 (Lecture 3) September 8, I this lecture, we ll cosider the aswer to oe of the most basic coutig problems i combiatorics Questio How may ways are there to choose a elemet subset of the set {,,,
More informationSince X n /n P p, we know that X n (n. Xn (n X n ) Using the asymptotic result above to obtain an approximation for fixed n, we obtain
Assigmet 9 Exercise 5.5 Let X biomial, p, where p 0, 1 is ukow. Obtai cofidece itervals for p i two differet ways: a Sice X / p d N0, p1 p], the variace of the limitig distributio depeds oly o p. Use the
More informationIt 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 informationBasics of Probability Theory (for Theory of Computation courses)
Basics of Probability Theory (for Theory of Computatio courses) Oded Goldreich Departmet of Computer Sciece Weizma Istitute of Sciece Rehovot, Israel. oded.goldreich@weizma.ac.il November 24, 2008 Preface.
More informationChapter 6 Sampling Distributions
Chapter 6 Samplig Distributios 1 I most experimets, we have more tha oe measuremet for ay give variable, each measuremet beig associated with oe radomly selected a member of a populatio. Hece we eed to
More information1 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 informationTwo phase stratified sampling with ratio and regression methods of estimation
CHAPTER  IV Two phase stratified samplig with ratio ad regressio methods of estimatio 4.1 Itroductio I sample survey a survey sampler might like to use a size variable x either (i) for stratificatio or
More informationStatistical Properties of OLS estimators
1 Statistical Properties of OLS estimators Liear Model: Y i = β 0 + β 1 X i + u i OLS estimators: β 0 = Y β 1X β 1 = Best Liear Ubiased Estimator (BLUE) Liear Estimator: β 0 ad β 1 are liear fuctio of
More informationModeling and Estimation of a Bivariate Pareto Distribution using the Principle of Maximum Entropy
Sri Laka Joural of Applied Statistics, Vol (53) Modelig ad Estimatio of a Bivariate Pareto Distributio usig the Priciple of Maximum Etropy Jagathath Krisha K.M. * Ecoomics Research Divisio, CSIRCetral
More informationDiscrete Mathematics for CS Spring 2008 David Wagner Note 22
CS 70 Discrete Mathematics for CS Sprig 2008 David Wager Note 22 I.I.D. Radom Variables Estimatig the bias of a coi Questio: We wat to estimate the proportio p of Democrats i the US populatio, by takig
More informationGeneralized Exponential Type Estimator for Population Variance in Survey Sampling
Revista Colombiaa de Estadística Juio 2014, volume 37, o. 1, pp. 211 a 222 Geeralized Expoetial Type Estimator for Populatio Variace i Survey Samplig Estimadores tipo expoecial geeralizado para la variaza
More informationResearch Article A TwoParameter RatioProductRatio Estimator Using Auxiliary Information
Iteratioal Scholarly Research Network ISRN Probability ad Statistics Volume, Article ID 386, 5 pages doi:.54//386 Research Article A TwoParameter RatioProductRatio Estimator Usig Auxiliary Iformatio
More informationTopic 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 informationInvestigating the Significance of a Correlation Coefficient using Jackknife Estimates
Iteratioal Joural of Scieces: Basic ad Applied Research (IJSBAR) ISSN 23074531 (Prit & Olie) http://gssrr.org/idex.php?joural=jouralofbasicadapplied 
More informationStat 421SP2012 Interval Estimation Section
Stat 41SP01 Iterval Estimatio Sectio 11.111. 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 informationChapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol DiscreteEvent System Simulation
Chapter Output Aalysis for a Sigle Model Baks, Carso, Nelso & Nicol DiscreteEvet System Simulatio Error Estimatio If {,, } are ot statistically idepedet, the S / is a biased estimator of the true variace.
More information3 Resampling Methods: The Jackknife
3 Resamplig Methods: The Jackkife 3.1 Itroductio I this sectio, much of the cotet is a summary of material from Efro ad Tibshirai (1993) ad Maly (2007). Here are several useful referece texts o resamplig
More information1 Introduction to reducing variance in Monte Carlo simulations
Copyright c 010 by Karl Sigma 1 Itroductio to reducig variace i Mote Carlo simulatios 11 Review of cofidece itervals for estimatig a mea I statistics, we estimate a ukow mea µ = E(X) of a distributio by
More informationEcon 325/327 Notes on Sample Mean, Sample Proportion, Central Limit Theorem, Chisquare Distribution, Student s t distribution 1.
Eco 325/327 Notes o Sample Mea, Sample Proportio, Cetral Limit Theorem, Chisquare Distributio, Studet s t distributio 1 Sample Mea By Hiro Kasahara We cosider a radom sample from a populatio. Defiitio
More informationLecture 7: Density Estimation: knearest Neighbor and Basis Approach
STAT 425: Itroductio to Noparametric Statistics Witer 28 Lecture 7: Desity Estimatio: knearest Neighbor ad Basis Approach Istructor: YeChi Che Referece: Sectio 8.4 of All of Noparametric Statistics.
More informationComparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3337 HIKARI Ltd, www.mhikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationGoodnessOfFit For The Generalized Exponential Distribution. Abstract
GoodessOfFit 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 informationo <Xln <X2n <... <X n < o (1.1)
Metrika, Volume 28, 1981, page 257262. 9 Viea. Estimatio Problems for Rectagular Distributios (Or the Taxi Problem Revisited) By J.S. Rao, Sata Barbara I ) Abstract: The problem of estimatig the ukow
More informationA 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 informationOn an Application of Bayesian Estimation
O a Applicatio of ayesia Estimatio KIYOHARU TANAKA School of Sciece ad Egieerig, Kiki Uiversity, Kowakae, HigashiOsaka, JAPAN Email: ktaaka@ifokidaiacjp EVGENIY GRECHNIKOV Departmet of Mathematics, auma
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationResampling 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 informationEstimating the Population Mean using Stratified Double Ranked Set Sample
Estimatig te Populatio Mea usig Stratified Double Raked Set Sample Mamoud Syam * Kamarulzama Ibraim Amer Ibraim AlOmari Qatar Uiversity Foudatio Program Departmet of Mat ad Computer P.O.Box (7) Doa State
More informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationThe standard deviation of the mean
Physics 6C Fall 20 The stadard deviatio of the mea These otes provide some clarificatio o the distictio betwee the stadard deviatio ad the stadard deviatio of the mea.. The sample mea ad variace Cosider
More informationECONOMETRIC THEORY. MODULE XIII Lecture  34 Asymptotic Theory and Stochastic Regressors
ECONOMETRIC THEORY MODULE XIII Lecture  34 Asymptotic Theory ad Stochastic Regressors Dr. Shalabh Departmet of Mathematics ad Statistics Idia Istitute of Techology Kapur Asymptotic theory The asymptotic
More informationTopic 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 informationIn this section we derive some finitesample 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 fiitesample 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 informationLecture 2: Monte Carlo Simulation
STAT/Q SCI 43: Itroductio to Resamplig ethods Sprig 27 Istructor: YeChi Che Lecture 2: ote Carlo Simulatio 2 ote Carlo Itegratio Assume we wat to evaluate the followig itegratio: e x3 dx What ca we do?
More informationECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015
ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a twoclass discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],
More informationGUIDELINES ON REPRESENTATIVE SAMPLING
DRUGS WORKING GROUP VALIDATION OF THE GUIDELINES ON REPRESENTATIVE SAMPLING DOCUMENT TYPE : REF. CODE: ISSUE NO: ISSUE DATE: VALIDATION REPORT DWGSGL001 002 08 DECEMBER 2012 Ref code: DWGSGL001 Issue
More informationControl Charts for Mean for NonNormally Correlated Data
Joural of Moder Applied Statistical Methods Volume 16 Issue 1 Article 5 51017 Cotrol Charts for Mea for NoNormally Correlated Data J. R. Sigh Vikram Uiversity, Ujjai, Idia Ab Latif Dar School of Studies
More information71. Chapter 4. Part I. Sampling Distributions and Confidence Intervals
71 Chapter 4 Part I. Samplig Distributios ad Cofidece Itervals 1 7 Sectio 1. Samplig Distributio 73 Usig Statistics Statistical Iferece: Predict ad forecast values of populatio parameters... Test hypotheses
More informationAnalytic Theory of Probabilities
Aalytic Theory of Probabilities PS Laplace Book II Chapter II, 4 pp 94 03 4 A lottery beig composed of umbered tickets of which r exit at each drawig, oe requires the probability that after i drawigs all
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture  9 Multicolliearity Dr Shalabh Departmet of Mathematics ad Statistics Idia Istitute of Techology Kapur Multicolliearity diagostics A importat questio that
More informationHypothesis Testing. Evaluation of Performance of Learned h. Issues. Tradeoff Between Bias and Variance
Hypothesis Testig Empirically evaluatig accuracy of hypotheses: importat activity i ML. Three questios: Give observed accuracy over a sample set, how well does this estimate apply over additioal samples?
More informationEconomics Spring 2015
1 Ecoomics 400  Sprig 015 /17/015 pp. 3038; Ch. 7.1.47. New Stata Assigmet ad ew MyStatlab assigmet, both due Feb 4th Midterm Exam Thursday Feb 6th, Chapters 17 of Groeber text ad all relevat lectures
More informationStatistics 511 Additional Materials
Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability
More informationEECS564 Estimation, Filtering, and Detection Hwk 2 Solns. Winter p θ (z) = (2θz + 1 θ), 0 z 1
EECS564 Estimatio, Filterig, ad Detectio Hwk 2 Sols. Witer 25 4. Let Z be a sigle observatio havig desity fuctio where. p (z) = (2z + ), z (a) Assumig that is a oradom parameter, fid ad plot the maximum
More informationµ and π p i.e. Point Estimation x And, more generally, the population proportion is approximately equal to a sample proportion
Poit Estimatio Poit estimatio is the rather simplistic (ad obvious) process of usig the kow value of a sample statistic as a approximatio to the ukow value of a populatio parameter. So we could for example
More informationEstimation of the Mean and the ACVF
Chapter 5 Estimatio of the Mea ad the ACVF A statioary process {X t } is characterized by its mea ad its autocovariace fuctio γ ), ad so by the autocorrelatio fuctio ρ ) I this chapter we preset the estimators
More informationEstimation of a population proportion March 23,
1 Social Studies 201 Notes for March 23, 2005 Estimatio of a populatio proportio Sectio 8.5, p. 521. For the most part, we have dealt with meas ad stadard deviatios this semester. This sectio of the otes
More informationKLMED8004 Medical statistics. Part I, autumn Estimation. We have previously learned: Population and sample. New questions
We have previously leared: KLMED8004 Medical statistics Part I, autum 00 How kow probability distributios (e.g. biomial distributio, ormal distributio) with kow populatio parameters (mea, variace) ca give
More informationSection 11.8: Power Series
Sectio 11.8: Power Series 1. Power Series I this sectio, we cosider geeralizig the cocept of a series. Recall that a series is a ifiite sum of umbers a. We ca talk about whether or ot it coverges ad i
More informationSimulation. Two Rule For Inverting A Distribution Function
Simulatio Two Rule For Ivertig A Distributio Fuctio Rule 1. If F(x) = u is costat o a iterval [x 1, x 2 ), the the uiform value u is mapped oto x 2 through the iversio process. Rule 2. If there is a jump
More information