A GENERALIZED LOGISTIC DISTRIBUTION
|
|
- Aldous French
- 5 years ago
- Views:
Transcription
1 A GENERALIZED LOGISTIC DISTRIBUTION SARALEES NADARAJAH AND SAMUEL KOTZ Received 11 October 2004 A generalized logistic distribution is proposed, based on the fact that the difference of two independent Gumbel-distributed random variables has the standard logistic distribution. 1. Introduction If X 1 and X 2 are independent Gumbel-distributed random variables with the common cdf Fx = exp { exp x }, 1.1 then it is well known that the difference Z = X 1 X 2 has the standard logistic distribution with the pdf f Z z = expz { 1+expz } for <z<. The properties of this distribution and its generalizations have been studied by several authors. Of particular eminence are the numerous papers on this topic by Professor N. Balakrishnan and his colleagues; see, for example, Balakrishnan [1, 2, 3], Balakrishnan and Aggarwala [4], Balakrishnan et al. [5, 7, 12], Balakrishnan and Chan [6], Balakrishnan and Joshi [8], Balakrishnan and Kocherlakota [9], Balakrishnan and Leung [10], BalakrishnanandMalik [11], Balakrishnanand Puthenpura [13], Balakrishnan and Sandhu [14], and Balakrishnan and Wong [15]. In this short note, we construct a new generalization of 1.2 bytakingx i, i = 1,2, to have the general Gumbel distribution with the cdf { F i x = exp exp x µ } i 1.3 for <x<, <µ i <, and > 0. This distribution which is also known as the extreme-value distribution of type I has received special attention in the probabilisticstatistical literature and in various applications in the second half of the twentieth century. Copyright 2005 Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences 2005: DOI: /IJMMS
2 3170 A generalized logistic distribution A recent book by Kotz and Nadarajah [16], which describes this distribution, lists over fifty applications ranging from accelerated life testing through to earthquakes, floods, horse racing, rainfall, queues in supermarkets, sea currents, wind speeds, and track race records to mention just a few. 2. The generalization The pdf corresponding to 1.3is f i x = 1 exp x µ { i exp exp and thus the pdf of Z = X 1 X 2 can be written as x µ } i, 2.1 f Z z = f 1 x f 2 x zdx = 1 exp x µ 1 σ 1 σ 1 exp x z µ 2 { exp exp x µ } 1 σ 1 { exp exp x z µ 2 } dx. 2.2 Setting y = exp x/σ 1, 2.2 can be expressed as where I denotes the integral f Z z = 1 µ1 exp + µ 2 + z I µ 1,µ 2,σ 1,, 2.3 σ 1 I µ 1,µ 2,σ 1, = 0 [ { y σ1/σ2 exp exp µ1 σ 1 y +exp µ2 + z y σ1/σ2 }] dy. 2.4 We refer to 2.3 asthegeneralized logistic distribution. The integral term in 2.4 isdifficult to calculate. However, for some particular choices of µ 1,µ 2,σ 1,, one can obtain the following explicit expressions. i If σ 1 = = σ, then by standard integration one can obtain 1 { exp µ1 /σ +exp µ 2 + z /σ } If, in addition, µ 1 = µ 2 = µ, then the above reduces to exp 2µ/σ { 1+expz/σ }
3 ii If σ 1 = 2, then one can show by [17, equation ] that α πα exp 8 αβ 2 4 { 2erfc αβ + αβ 2 erfc 2 S. Nadarajah and S. Kotz 3171 } αβ α2 β 2 4, 2.7 where α = exp{µ 2 + z/ }, β = exp{µ 1 /2 }, anderfc, denotes the complementary error function defined by erfcx = 1 2 x exp t 2 dt. 2.8 π 0 iii If 0 <σ 1 / = p/q < 1wherep 1andq 1 are co-prime integers, then one can show by [17, equation ] that q 1 j=0 α j p1 + j Γ 1+ j! q p+1 F q 1, p,1+ β 1+p1+j/q p1 + j q ; q,1+ j; 1q p p α q q q β p, 2.9 where α = exp{µ 2 + z/ }, β = expµ 1 /σ 1, k,a denotes the sequence k,a = a k, a +1 k,..., a + k 1, 2.10 k mf n denotes the generalized hypergeometric function defined by mf n α1,...,α m ;β 1,...,β n ;x = k=0 α1 k α m k β1 k β x k n k k!, 2.11 and c k = cc +1 c + k 1 denotes the ascending factorial. iv If σ 1 / = p/q > 1wherep 1andq 1 are coprime integers, then one can showagain by [17, equation ]that p 1 j=0 q β j Γ 1+ pj! q+1 F p 1, q1 + j p q,1+ α 1+q1+j/p q1 + j p ; p,1+ j; 1p q q β p p p α q, 2.12 where α = exp{µ 2 + z/ } and β = expµ 1 /σ 1.
4 3172 A generalized logistic distribution 0.3 f x x σ 1 / = 0.2 σ 1 / = 1 σ 1 / = 2 σ 1 / = 5 σ 1 / = 10 Figure 2.1. The generalized logistic pdf 2.3forσ 1 / = 0.2,1,2,5,10, = 1, µ 1 = 0, and µ 2 = f x x σ 1 / = 0.2 σ 1 / = 1 σ 1 / = 2 σ 1 / = 5 σ 1 / = 10 Figure 2.2. The generalized logistic pdf 2.3forσ 1 / = 0.2,1,2,5,10, = 1, µ 1 = 1, and µ 2 = 0. Figures 2.1 and 2.2 illustrate possible shapes of the pdf 2.3 for selected values of µ 1,µ 2,σ 1,. The magnitude of σ 1 / clearly controls the shape of the pdf. In fact, if µ 1 = 0, then f Z z 1 { } µ2 + z µ2 + z exp exp exp 2.13
5 S. Nadarajah and S. Kotz 3173 as σ 1 / 0. Also, f z 0foreveryz 0, asσ 1 /. On the other hand, if µ 1 0, then f z 0foreveryz 0, irrespective of whether σ 1 / 0orσ 1 /. 3. Applications The standard logistic distributiongiven by 1.2 has important uses in describing growth and as a substitute for the normal distribution. It has also attracted interesting applications in the modeling of the dependence of chronic obstructive respiratory disease prevalence on smoking and age, degrees of pneumoconiosis in coal miners, geological issues, hemolytic uremic syndrome data for children, physiochemical phenomenon, psychological issues, survival time of diagnosed leukemia patients, and weight gain data. The main feature of the generalized logistic distribution in 2.3 is that new parameters are introduced to control both location and scale. Thus, 2.3 allowsforagreaterdegreeofflexibility and we can expect this to be useful in many more practical situations. References [1] N. Balakrishnan, Order statistics from the half logistic distribution, J. Statist. Comput. Simulation , no. 4, [2], Approximate maximum likelihood estimation for a generalized logistic distribution, J. Statist. Plann. Inference , no. 2, [3] N. Balakrishnan ed., Handbook of the Logistic Distribution, Statistics: Textbooks and Monographs, vol. 123, Marcel Dekker, New York, [4] N. Balakrishnan and R. Aggarwala, Relationships for moments of order statistics from the righttruncated generalized half logistic distribution, Ann. Inst. Statist. Math , no. 3, [5] N. Balakrishnan, M. Ahsanullah, and P. S. Chan, On the logistic record values and associated inference, J. Appl. Statist. Sci , no. 3, [6] N. Balakrishnan and P. S. Chan, Estimation for the scaled half logistic distribution under type II censoring, Comput. Statist. Data Anal , no. 2, [7] N. Balakrishnan, S. S. Gupta, and S. Panchapakesan, Estimation of the mean and standard deviation of the logistic distribution based on multiply type-ii censored samples, Statistics , no. 1-2, [8] N. Balakrishnan and P. C. Joshi, Means, variances and covariances of order statistics from symmetrically truncated logistic distribution, J. Statist. Res , no. 1-2, [9] N. Balakrishnan and S. Kocherlakota, On the moments of order statistics from the doubly truncated logistic distribution, J. Statist. Plann. Inference , no. 1, [10] N. Balakrishnan and M. Y. Leung, Means, variances and covariances of order statistics, BLUEs for the type I generalized logistic distribution, and some applications, Comm. Statist. Simulation Comput , no. 1, [11] N. Balakrishnan and H. J. Malik, Moments of order statistics from truncated log-logistic distribution, J. Statist. Plann. Inference , no. 2, [12] N. Balakrishnan, H. J. Malik, and S. Puthenpura, Best linear unbiased estimation of location and scale parameters of the log-logistic distribution, Comm. Statist. Theory Methods , no. 12, [13] N. Balakrishnan and S. Puthenpura, Best linear unbiased estimators of location and scale parameters of the half logistic distribution, J. Statist. Comput. Simulation , no. 3-4,
6 3174 A generalized logistic distribution [14] N. Balakrishnan and R. A. Sandhu, Recurrence relations for single and product moments of order statistics from a generalized half logistic distribution with applications to inference, J.Statist. Comput. Simulation , no. 4, [15] N. Balakrishnan and K. H. T. Wong, Best linear unbiased estimation of location and scale parameters of the half-logistic distribution based on type II censored samples, Amer. J. Math. Management Sci , no. 1-2, [16] S. Kotz and S. Nadarajah, Extreme Value Distributions. Theory and Applications, Imperial College Press, London, [17] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Vol. 1. Elementary Functions, Gordon & Breach Science, New York, [18], Integrals and Series. Vol. 2. Special Functions, Gordon & Breach Science, New York, [19], Integrals and Series. Vol. 3. More Special Functions, Gordon & Breach Science, New York, Saralees Nadarajah: Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA address: snadaraj@chuma1.cas.usf.edu Samuel Kotz: Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052, USA address: kotz@seas.gwu.edu
7 Mathematical Problems in Engineering Special Issue on Time-Dependent Billiards Call for Papers This subject has been extensively studied in the past years for one-, two-, and three-dimensional space. Additionally, such dynamical systems can exhibit a very important and still unexplained phenomenon, called as the Fermi acceleration phenomenon. Basically, the phenomenon of Fermi acceleration FA is a process in which a classical particle can acquire unbounded energy from collisions with a heavy moving wall. This phenomenon was originally proposed by Enrico Fermi in 1949 as a possible explanation of the origin of the large energies of the cosmic particles. His original model was then modified and considered under different approaches and using many versions. Moreover, applications of FA have been of a large broad interest in many different fields of science including plasma physics, astrophysics, atomic physics, optics, and time-dependent billiard problems and they are useful for controlling chaos in Engineering and dynamical systems exhibiting chaos both conservative and dissipative chaos. We intend to publish in this special issue papers reporting research on time-dependent billiards. The topic includes both conservative and dissipative dynamics. Papers discussing dynamical properties, statistical and mathematical results, stability investigation of the phase space structure, the phenomenon of Fermi acceleration, conditions for having suppression of Fermi acceleration, and computational and numerical methods for exploring these structures and applications are welcome. To be acceptable for publication in the special issue of Mathematical Problems in Engineering, papers must make significant, original, and correct contributions to one or more of the topics above mentioned. Mathematical papers regarding the topics above are also welcome. Authors should follow the Mathematical Problems in Engineering manuscript format described at Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at mts.hindawi.com/ according to the following timetable: Guest Editors Edson Denis Leonel, Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Avenida 24A, 1515 Bela Vista, Rio Claro, SP, Brazil ; edleonel@rc.unesp.br Alexander Loskutov, Physics Faculty, Moscow State University, Vorob evy Gory, Moscow , Russia; loskutov@chaos.phys.msu.ru Manuscript Due December 1, 2008 First Round of Reviews March 1, 2009 Publication Date June 1, 2009 Hindawi Publishing Corporation
A GENERALIZED LOGISTIC DISTRIBUTION
A GENERALIZED LOGISTIC DISTRIBUTION SARALEES NADARAJAH AND SAMUEL KOTZ Received 11 October 2004 A generalized logistic distribution is proposed, based on the fact that the difference of two independent
More informationON THE COEFFICIENTS OF VARIATION OF UPTIME AND DOWNTIME IN MANUFACTURING EQUIPMENT
ON THE COEFFICIENTS OF VARIATION OF UPTIME AND DOWNTIME IN MANUFACTURING EQUIPMENT JINGSHAN LI AND SEMYON M. MEERKOV Received 28 November 24 It was reported in the literature that the coefficients of variation
More informationREMARKS ON CERTAIN SELECTED FIXED POINT THEOREMS
IJMMS 29:1 (2002) 43 46 PII. S016117120200491X http://ijmms.hindawi.com Hindawi Publishing Corp. REMARKS ON CERTAIN SELECTED FIXED POINT THEOREMS M. IMDAD Received 8 July 1999 and in revised form 27 March
More informationPROPERTIES OF ITS ABSOLUTE VALUES
Intn. J. Math. Math. Sci. Vol. 4 No. 4 (1981) 641-647 641 ON HOLOMORPHIC FUNCTIONS WITH CERTAIN EXTREMAL PROPERTIES OF ITS ABSOLUTE VALUES DIETER SCHMERSAU Mathematisches Institut der Freien Universitt
More informationINITIAL STRESS AT THE EARTH S CORE-MANTLE BOUNDARY
I nternat. J. Math. & Math. Si. Vol. 3 No. 3 (1980) 591-598 591 REFLECTION AND TRANSMISSION OF SEISMIC WAVES UNDER INITIAL STRESS AT THE EARTH S CORE-MANTLE BOUNDARY SUKHENDU DEY and SUSHIL KUMAR ADDY
More informationOptimum Workforce Scheduling Under the (14, 21) Days-Off Timetable
JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, 6(3), 191 199 Copyright c 00, Lawrence Erlbaum Associates, Inc. Optimum Workforce Scheduling Under the (14, 1) Days-Off Timetable HESHAM K. ALFARES
More informationGRACEFUL NUMBERS. KIRAN R. BHUTANI and ALEXANDER B. LEVIN. Received 14 May 2001
IJMMS 29:8 2002 495 499 PII S06720200765 htt://immshindawicom Hindawi Publishing Cor GRACEFUL NUMBERS KIRAN R BHUTANI and ALEXANDER B LEVIN Received 4 May 200 We construct a labeled grah Dn that reflects
More informationResearch Article Sufficient Conditions for Janowski Starlikeness
Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2007, Article ID 62925, 7 pages doi:10.1155/2007/62925 Research Article Sufficient Conditions for Janowski
More informationCOMPUTATIONAL PROOFS OF CONGRUENCES FOR 2-COLORED FROBENIUS PARTITIONS
IJMMS 29:6 2002 333 340 PII. S0161171202007342 http://ijmms.hindawi.com Hindawi Publishing Corp. COMPUTATIONAL PROOFS OF CONGRUENCES FOR 2-COLORED FROBENIUS PARTITIONS DENNIS EICHHORN and JAMES A. SELLERS
More informationNEW FILTERING TECHNIQUE FOR THE IMPULSIVE NOISE REDUCTION IN COLOR IMAGES
NEW FILTERING TECHNIQUE FOR THE IMPULSIVE NOISE REDUCTION IN COLOR IMAGES B. SMOLKA, A. CHYDZINSKI, K. N. PLATANIOTIS, AND A. N. VENETSANOPOULOS Received 31 October 2001 We present a novel approach to
More informationA NOTE OF EQUIVALENCE CLASSES OF MATRICES
I nternat. J. Math. Math. Sci. Vol. 4 No. 2 (1981) 279-287 279 A NOTE OF EQUIVALENCE CLASSES OF MATRICES OVER A FINITE FIELD J.V. BRAWLEY Department of Mathematical Sciences, Clemson University Clemson,
More informationFORWARD-BACKWARD RESOLVENT SPLITTING METHODS FOR GENERAL MIXED VARIATIONAL INEQUALITIES
IJMMS 2003:43, 2759 2770 PII. S0161171203210462 http://ijmms.hindawi.com Hindawi Publishing Corp. FORWARD-BACKWARD RESOLVENT SPLITTING METHODS FOR GENERAL MIXED VARIATIONAL INEQUALITIES MUHAMMAD ASLAM
More informationSTARLIKENESS ASSOCIATED WITH PARABOLIC REGIONS
STARLIKENESS ASSOCIATED WITH PARABOLIC REGIONS ROSIHAN M. ALI Received 29 April 2004 and in revised form 15 September 2004 A parabolic starlike function f of order ρ in the unit disk is characterized by
More informationFIXED-WIDTH CONFIDENCE INTERVAL FOR A LOGNORMAL MEAN
IJMMS 9:3 00 143 153 PII. S01611710011055 http://ijmms.hindawi.com Hindawi Publishing Corp. FIXED-WIDTH CONFIDENCE INTERVAL FOR A LOGNORMAL MEAN MAKOTO AOSHIMA and ZAKKULA GOVINDARAJULU Received 5 October
More informationA NOTE ON COMPUTING THE GENERALIZED INVERSE A (2)
IJMMS 31:8 (2002 497 507 PII. S0161171202013169 http://ijmms.hindawi.com Hindawi Publishing Corp. A NOTE ON COMPUTING THE GENERALIZED INVERSE A (2 OF A MATRIX A XIEZHANG LI and YIMIN WEI Received 10 May
More informationNOTE ON KKM MAPS AND APPLICATIONS
NOTE ON KKM MAPS AND APPLICATIONS Y.Q.CHEN,Y.J.CHO,J.K.KIM,ANDB.S.LEE Received 6 March 2005; Revised 20 July 2005; Accepted 11 August 2005 We apply the KKM technique to study fixed point theory, minimax
More informationResearch Article Determinant and Inverse of Meet and Join Matrices
Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2007, Article ID 37580, 11 pages doi:10.1155/2007/37580 Research Article Determinant and Inverse of
More informationABS..TACT. In this expository paper, it is shown that if an entire function of
lvmat. J. Math. Math. S. Vol. 4 No. 2 (1981) 311-381 371 YET ANOTHER CHARACTERIZATION OF THE SINE FUNCTION ROBERT GERVAIS Dpartement de Mathmatiques Co118e Llitaire royal de Saint-Jean Saint-Jean, Quebec,
More informationResearch Article Stochastic Finite Element Technique for Stochastic One-Dimension Time-Dependent Differential Equations with Random Coefficients
Hindawi Publishing Corporation Differential Equations and Nonlinear Mechanics Volume 7, Article ID 4857, 6 pages doi:5/7/4857 Research Article Stochastic Finite Element Technique for Stochastic One-Dimension
More informationGo(X) [Y (X) min(y) 0}. In
Internat. J. Math. & Math. Sci. Vol. 9 No. 3 (1986) 605-616 605 THE SEMIGROUP OF NONEMPTY FINITE SUBSETS OF INTEGERS REUBEN SPAKE Department of Mathematics, University of California Davis, California 95616
More informationComputation of Signal to Noise Ratios
MATCH Communications in Mathematical in Computer Chemistry MATCH Commun. Math. Comput. Chem. 57 7) 15-11 ISS 34-653 Computation of Signal to oise Ratios Saralees adarajah 1 & Samuel Kotz Received May,
More informationA Study of Five Parameter Type I Generalized Half Logistic Distribution
Pure and Applied Mathematics Journal 2017; 6(6) 177-181 http//www.sciencepublishinggroup.com/j/pamj doi 10.11648/j.pamj.20170606.14 ISSN 2326-9790 (Print); ISSN 2326-9812 (nline) A Study of Five Parameter
More informationEXPLICIT EXPRESSIONS FOR MOMENTS OF χ 2 ORDER STATISTICS
Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 3 (28), No. 3, pp. 433-444 EXPLICIT EXPRESSIONS FOR MOMENTS OF χ 2 ORDER STATISTICS BY SARALEES NADARAJAH Abstract Explicit closed
More informationMicrowave Assisted Ignition to Achieve Combustion Synthesis
JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, 5(3), 151 164 Copyright c 2001, Lawrence Erlbaum Associates, Inc. Microwave Assisted Ignition to Achieve Combustion Synthesis E. BALAKRISHNAN* balak@squ.edu.om
More informationRELATIONS FOR MOMENTS OF PROGRESSIVELY TYPE-II RIGHT CENSORED ORDER STATISTICS FROM ERLANG-TRUNCATED EXPONENTIAL DISTRIBUTION
STATISTICS IN TRANSITION new series, December 2017 651 STATISTICS IN TRANSITION new series, December 2017 Vol. 18, No. 4, pp. 651 668, DOI 10.21307/stattrans-2017-005 RELATIONS FOR MOMENTS OF PROGRESSIVELY
More informationGyeongsang National University
Internat. J. Math. & Math. Sci. VOL. 20 NO. 2 (1997) 249-256 249 COINCIDENCE THEOREMS FOR NONLINEAR HYBRID CONTRACTIONS Y.J. CHO B. FISHER G.S. GENGA Department of Mathematics and Computer Science Deptartment
More informationTransmuted Exponentiated Gumbel Distribution (TEGD) and its Application to Water Quality Data
Transmuted Exponentiated Gumbel Distribution (TEGD) and its Application to Water Quality Data Deepshikha Deka Department of Statistics North Eastern Hill University, Shillong, India deepshikha.deka11@gmail.com
More informationThis article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
More information{ zf"(z)} > 8; 0 < 8 < I} S(a,8)" {flf e S, SPIRAL LIKE INTEGRAL OPERATORS. {f[f:d / C, f to be regular, univalent and f(0) o, f (0) I},
Intnat. J. Mh. Mah. Sci. Vol. 4 No. 2 (1981) 337-551 337 SPIRAL LIKE INTEGRAL OPERATORS SHYANI K. BAJPAI D. epartamento de Matematica Universidade de Brasilia Instituto de Ciencias Exactas 709 I0 Brasilia-DF-BRASlL
More informationON THE LAUWERIER FORMULATION OF THE TEMPERATURE FIELD PROBLEM IN OIL STRATA
ON THE LAUWERIER FORMULATION OF THE TEMPERATURE FIELD PROBLEM IN OIL STRATA LYUBOMIR BOYADJIEV, OGNIAN KAMENOV, AND SHYAM KALLA Received 3 January 5 Dedicated to Professor Dr. Ivan Dimovski, Institute
More informationCOMPLETELY CONTRACTIVE MAPS BETWEEN C -ALGEBRAS
IJMMS 32:8 2002) 507 513 PII. S0161171202111331 http://mms.hindawi.com Hindawi Publishing Corp. COMPLETELY CONTRACTIVE MAPS BETWEEN C -ALGEBRAS W. T. SULAIMAN Received 15 November 2001 We give a simple
More informationON EXTENDED TYPE I GENERALIZED LOGISTIC DISTRIBUTION
IJMMS 2004:57, 3069 3074 PII. S0161171204309014 http://ijmms.hindawi.com Hindawi Publishing Corp. ON EXTENDED TYPE I GENERALIZED LOGISTIC DISTRIBUTION A. K. OLAPADE Received 2 September 2003 We consider
More informationTime-dependent properties in two-dimensional and Hamiltonian mappings
Eur. Phys. J. Special Topics 223, 2953 2958 (2014) EDP Sciences, Springer-Verlag 2014 DOI: 10.1140/epjst/e2014-02308-6 THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS Regular Article Time-dependent properties
More informationResearch Article Numerical Effectiveness of Models and Methods of Integration of the Equations of Motion of a Car
Hindawi Publishing Corporation Differential Equations and Nonlinear Mechanics Volume 2007, Article ID 49157, 13 pages doi:10.1155/2007/49157 Research Article Numerical Effectiveness of Models and Methods
More informationEstimation in an Exponentiated Half Logistic Distribution under Progressively Type-II Censoring
Communications of the Korean Statistical Society 2011, Vol. 18, No. 5, 657 666 DOI: http://dx.doi.org/10.5351/ckss.2011.18.5.657 Estimation in an Exponentiated Half Logistic Distribution under Progressively
More informationEstimation for generalized half logistic distribution based on records
Journal of the Korean Data & Information Science Society 202, 236, 249 257 http://dx.doi.org/0.7465/jkdi.202.23.6.249 한국데이터정보과학회지 Estimation for generalized half logistic distribution based on records
More informationPoint and Interval Estimation for Gaussian Distribution, Based on Progressively Type-II Censored Samples
90 IEEE TRANSACTIONS ON RELIABILITY, VOL. 52, NO. 1, MARCH 2003 Point and Interval Estimation for Gaussian Distribution, Based on Progressively Type-II Censored Samples N. Balakrishnan, N. Kannan, C. T.
More informationResearch Article Scaling Properties of a Hybrid Fermi-Ulam-Bouncer Model
Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2009, Article ID 23857, 3 pages doi:0.55/2009/23857 Research Article Scaling Properties of a Hybrid Fermi-Ulam-Bouncer Model Diego
More informationA NOTE ON WELL-POSED NULL AND FIXED POINT PROBLEMS
A NOTE ON WELL-POSED NULL AND FIXED POINT PROBLEMS SIMEON REICH AND ALEXANDER J. ZASLAVSKI Received 16 October 2004 We establish generic well-posedness of certain null and fixed point problems for ordered
More informationEstimation for Mean and Standard Deviation of Normal Distribution under Type II Censoring
Communications for Statistical Applications and Methods 2014, Vol. 21, No. 6, 529 538 DOI: http://dx.doi.org/10.5351/csam.2014.21.6.529 Print ISSN 2287-7843 / Online ISSN 2383-4757 Estimation for Mean
More informationON A ZONAL POLYNOMIAL INTEGRAL
ON A ZONAL POLYNOMIAL INTEGRAL A. K. GUPTA AND D. G. KABE Received September 00 and in revised form 9 July 003 A certain multiple integral occurring in the studies of Beherens-Fisher multivariate problem
More informationSOME RESULTS ON FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS IN COMPLETE METRIC SPACES
IJMMS 30:6 2002 319 325 PII. S0161171202110350 http://ijmms.hindawi.com Hindawi Publishing Corp. SOME RESULTS ON FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS IN COMPLETE METRIC SPACES JEONG SHEOK UME,
More informationOn Five Parameter Beta Lomax Distribution
ISSN 1684-840 Journal of Statistics Volume 0, 01. pp. 10-118 On Five Parameter Beta Lomax Distribution Muhammad Rajab 1, Muhammad Aleem, Tahir Nawaz and Muhammad Daniyal 4 Abstract Lomax (1954) developed
More informationarxiv: v1 [math.at] 15 Aug 2017
GENERALIZED JIANG AND GOTTLIEB GROUPS MAREK GOLASIŃSKI AND THIAGO DE MELO arxiv:1708.04708v1 [math.at] 15 Aug 2017 Abstract. Given a map f: X Y, we extend a Gottlieb s result to the generalized Gottlieb
More informationEstimation of Parameters of the Weibull Distribution Based on Progressively Censored Data
International Mathematical Forum, 2, 2007, no. 41, 2031-2043 Estimation of Parameters of the Weibull Distribution Based on Progressively Censored Data K. S. Sultan 1 Department of Statistics Operations
More informationRELIABILITY FOR SOME BIVARIATE BETA DISTRIBUTIONS
RELIABILITY FOR SOME BIVARIATE BETA DISTRIBUTIONS SARALEES NADARAJAH Received 24 June 24 In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability
More informationHOMOGENEOUS BOUNDED DOMAINS IN C 4 AND Cs
Internat. J. Math. & Math. Sci. VOL. 15 NO. 4 (1992) 741-752 741 NEW REPRESENTATION OF THE NON-SYMMETRIC HOMOGENEOUS BOUNDED DOMAINS IN C 4 AND Cs GR. TSAGAS and G. DIMOU Division of Mathematics Department
More informationISI Web of Knowledge (Articles )
ISI Web of Knowledge (Articles 1 -- 18) Record 1 of 18 Title: Estimation and prediction from gamma distribution based on record values Author(s): Sultan, KS; Al-Dayian, GR; Mohammad, HH Source: COMPUTATIONAL
More informationConsequences of Quadratic Frictional Force on the One Dimensional Bouncing Ball Model
Consequences of Quadratic Frictional Force on the One Dimensional Bouncing Ball Model Edson D. Leonel 1 and Danila F. Tavares 2 1 Departamento de Estatistica, Matemdtica Aplicada e Computaqao, Universidade
More informationk-i (--1)"-kA"y(t) A pi(t)zy(t), 0 < < T, (1.1) i=0 Throughout this paper, the interval notation in expressions such k-1 (--1)"-A"y(t)
Internat. J. Math. & Math. Sci. VOL. 16 NO. (1993) 169-176 169 A FOCAL BOUNDARY VALUE PROBLEM FOR DIFFERENCE EQUATIONS CATHRYN DENNY and DARREL HANKERSON Department of Algebra, Combinatorics, and Analysis
More informationResearch Article On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 27, Article ID 7375, 5 pages doi:1.1155/27/7375 Research Article On a Class of Integrals Involving a
More informationAn Analysis of Record Statistics based on an Exponentiated Gumbel Model
Communications for Statistical Applications and Methods 2013, Vol. 20, No. 5, 405 416 DOI: http://dx.doi.org/10.5351/csam.2013.20.5.405 An Analysis of Record Statistics based on an Exponentiated Gumbel
More informationTransformation formulas for the generalized hypergeometric function with integral parameter differences
Transformation formulas for the generalized hypergeometric function with integral parameter differences A. R. Miller Formerly Professor of Mathematics at George Washington University, 66 8th Street NW,
More informationz2)p,(z) (where p,(x)is a Lcgcndrc polynomial). The corresponding approximation degrees are given.
Internat. 3. Math. & Math. Sci. VOL. 19 NO. 2 (1996) 279-286 279 ON APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY QUASIoHERMITE INTERPOLATION G. MIN CECM, Department of Mathematics Statistics Simon
More informationExact Inference for the Two-Parameter Exponential Distribution Under Type-II Hybrid Censoring
Exact Inference for the Two-Parameter Exponential Distribution Under Type-II Hybrid Censoring A. Ganguly, S. Mitra, D. Samanta, D. Kundu,2 Abstract Epstein [9] introduced the Type-I hybrid censoring scheme
More informationBLOWUP OF SOLUTIONS OF A NONLINEAR WAVE EQUATION
BLOWUP OF SOLUTIONS OF A NONLINEAR WAVE EQUATION ABBES BENAISSA AND SALIM A. MESSAOUDI Received 4 April 2001 and in revised form 20 October 2001 We establish a blowup result to an initial boundary value
More informationA NEW CHAOTIC ATTRACTOR FROM 2D DISCRETE MAPPING VIA BORDER-COLLISION PERIOD-DOUBLING SCENARIO
A NEW CHAOTIC ATTRACTOR FROM D DISCRETE MAPPING VIA BORDER-COLLISION PERIOD-DOUBLING SCENARIO ZERAOULIA ELHADJ Received 1 April 5 The following map is studied: (, ) (1 + a( )+,b). It is proved numericall
More informationInternational Journal of Pure and Applied Sciences and Technology
Int. J. Pure Appl. Sci. Technol., 9(1) (2012), pp. 5260 International Journal of Pure and Applied Sciences and Technology ISSN 2229 6107 Available online at www.ijopaasat.in Research Paper Development
More informationARNOLD AND STRAUSS S BIVARIATE EXPONENTIAL DISTRIBUTION PRODUCTS AND RATIOS. Saralees Nadarajah and Dongseok Choi (Received February 2005)
NEW ZEALAND JOURNAL OF MATHEMATICS Volume 35 6), 189 199 ARNOLD AND STRAUSS S BIVARIATE EXPONENTIAL DISTRIBUTION PRODUCTS AND RATIOS Saralees Nadarajah and Dongseok Choi Received February 5) Abstract.
More informationTHE BIVARIATE F 3 -BETA DISTRIBUTION. Saralees Nadarajah. 1. Introduction
Commun. Korean Math. Soc. 21 2006, No. 2, pp. 363 374 THE IVARIATE F 3 -ETA DISTRIUTION Saralees Nadarajah Abstract. A new bivariate beta distribution based on the Appell function of the third kind is
More informationPhysica A. Separation of particles in time-dependent focusing billiards
Physica A 389 (2010) 5408 5415 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Separation of particles in time-dependent focusing billiards Alexander
More informationA NONLINEAR DIFFERENTIAL EQUATION INVOLVING REFLECTION OF THE ARGUMENT
ARCHIVUM MATHEMATICUM (BRNO) Tomus 40 (2004), 63 68 A NONLINEAR DIFFERENTIAL EQUATION INVOLVING REFLECTION OF THE ARGUMENT T. F. MA, E. S. MIRANDA AND M. B. DE SOUZA CORTES Abstract. We study the nonlinear
More informationOn the Ratio of Rice Random Variables
JIRSS 9 Vol. 8, Nos. 1-, pp 61-71 On the Ratio of Rice Random Variables N. B. Khoolenjani 1, K. Khorshidian 1, 1 Departments of Statistics, Shiraz University, Shiraz, Iran. n.b.khoolenjani@gmail.com Departments
More informationPseudo-Boolean Functions, Lovász Extensions, and Beta Distributions
Pseudo-Boolean Functions, Lovász Extensions, and Beta Distributions Guoli Ding R. F. Lax Department of Mathematics, LSU, Baton Rouge, LA 783 Abstract Let f : {,1} n R be a pseudo-boolean function and let
More informationN (Uke) (1.1) A DOUBLE CHAIN OF COUPLED CIRCUITS IN ANALOGY WITH MECHANICAL LATTICES. Uke
Internat. J. Math. & Math. Sci. VOL. 14 NO. 2 (1991) 403-406 403 A DOUBLE CHAIN OF COUPLED CIRCUITS IN ANALOGY WITH MECHANICAL LATTICES J.N. BOYD and P.N. RAYCHOWDHURY Department of Mathematical Sciences
More informationThe Complementary Exponential-Geometric Distribution Based On Generalized Order Statistics
Applied Mathematics E-Notes, 152015, 287-303 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ The Complementary Exponential-Geometric Distribution Based On Generalized
More informationExact Linear Likelihood Inference for Laplace
Exact Linear Likelihood Inference for Laplace Prof. N. Balakrishnan McMaster University, Hamilton, Canada bala@mcmaster.ca p. 1/52 Pierre-Simon Laplace 1749 1827 p. 2/52 Laplace s Biography Born: On March
More information(ei0 AN EXAMPLE OF A BLOCH FUNCTION. KEY WORDS AND PHRASES. Bloch function. I nternat. J. Math. & Math. Sci.
I nternat. J. Math. & Math. Sci. Vol. 2 (1979) 147-150 147 AN EXAMPLE OF A BLOCH FUNCTION RICHARD M. TIMONEY Department of Mathematics Indiana University Bloomington, Indiana 47401 U.S.A. (Received November
More informationOn Characterizations of the Half Logistic Distribution
On Characterizations of the Half Logistic Distribution A.K. Olapade Department of Mathematics Obafemi Awolowo University Ile-Ife, Nigeria. E-mail: akolapad@oauife.edu.ng Abstract Characterizations of the
More informationA Short Note on a Nonlinear System Vibrations under Two Non-Ideal Excitations
J. L. Palacios Universidade Regional Integrada de Santo Ângelo Departamento de Ciências Exatas e da Terra-URI C.P. 03 9880-470 Santo Ângelo, RS. Brazil jfelix@urisan.tche.br J. M. Balthazar Universidade
More informationContinuous Univariate Distributions
Continuous Univariate Distributions Volume 2 Second Edition NORMAN L. JOHNSON University of North Carolina Chapel Hill, North Carolina SAMUEL KOTZ University of Maryland College Park, Maryland N. BALAKRISHNAN
More informationESTIMATES ON THE NUMBER OF LIMIT CYCLES OF A GENERALIZED ABEL EQUATION
Manuscript submitted to Website: http://aimsciences.org AIMS Journals Volume 00, Number 0, Xxxx XXXX pp. 000 000 ESTIMATES ON THE NUMBER OF LIMIT CYCLES OF A GENERALIZED ABEL EQUATION NAEEM M.H. ALKOUMI
More informationSpherically Symmetric Logistic Distribution
Journal of Multivariate Analysis 7, 2226 (999) Article ID jmva.999.826, available online at httpwww.idealibrary.com on Spherically Symmetric Logistic Distribution Nikolai A. Volodin The Australian Council
More informationA Discrete Stress-Strength Interference Model With Stress Dependent Strength Hong-Zhong Huang, Senior Member, IEEE, and Zong-Wen An
118 IEEE TRANSACTIONS ON RELIABILITY VOL. 58 NO. 1 MARCH 2009 A Discrete Stress-Strength Interference Model With Stress Dependent Strength Hong-Zhong Huang Senior Member IEEE and Zong-Wen An Abstract In
More informationInterpolation of Rational Functions on a Geometric Mesh
CONSTRUCTIVE THEORY OF FUNCTIONS, Varna 5 additional information (to be provided by the publisher) Interpolation of Rational Functions on a Geometric Mesh Dimitar K. Dimitrov We discuss the Newton-Gregory
More informationMethod of Moments. which we usually denote by X or sometimes by X n to emphasize that there are n observations.
Method of Moments Definition. If {X 1,..., X n } is a sample from a population, then the empirical k-th moment of this sample is defined to be X k 1 + + Xk n n Example. For a sample {X 1, X, X 3 } the
More informationA class of probability distributions for application to non-negative annual maxima
Hydrol. Earth Syst. Sci. Discuss., doi:.94/hess-7-98, 7 A class of probability distributions for application to non-negative annual maxima Earl Bardsley School of Science, University of Waikato, Hamilton
More informationStatistical Inference Using Progressively Type-II Censored Data with Random Scheme
International Mathematical Forum, 3, 28, no. 35, 1713-1725 Statistical Inference Using Progressively Type-II Censored Data with Random Scheme Ammar M. Sarhan 1 and A. Abuammoh Department of Statistics
More informationPolyexponentials. Khristo N. Boyadzhiev Ohio Northern University Departnment of Mathematics Ada, OH
Polyexponentials Khristo N. Boyadzhiev Ohio Northern University Departnment of Mathematics Ada, OH 45810 k-boyadzhiev@onu.edu 1. Introduction. The polylogarithmic function [15] (1.1) and the more general
More informationOberwolfach Preprints
Oberwolfach Preprints OWP 2013-23 CLEONICE F. BRACCIALI AND JUAN JOSÉ MORENO- BALCÁZAR Mehler-Heine Asymptotics of a Class of Generalized Hypergeometric Polynomials Mathematisches Forschungsinstitut Oberwolfach
More informationAlpha-Skew-Logistic Distribution
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 9-765X Volume 0, Issue Ver VI (Jul-Aug 0), PP 6-6 Alpha-Sew-Logistic Distribution Partha Jyoti Haaria a and Subrata Charaborty b a Department
More informationResearch Article Strong Convergence Bound of the Pareto Index Estimator under Right Censoring
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 200, Article ID 20956, 8 pages doi:0.55/200/20956 Research Article Strong Convergence Bound of the Pareto Index Estimator
More informationOn a Generalization of Weibull Distribution and Its Applications
International Journal of Statistics and Applications 26, 6(3): 68-76 DOI:.5923/j.statistics.2663. On a Generalization of Weibull Distribution and Its Applications M. Girish Babu Department of Statistics,
More informationASYMPTOTIC EXPANSIONS
Monografías del Seminario Matemático García de Galdeano 33, 145 15 (6) ASYMPTOTIC EXPANSIONS OF THE APPELL S FUNCTION F José Luis López and María Esther García Abstract. The second Appell s hypergeometric
More informationDepartment of Statistical Science FIRST YEAR EXAM - SPRING 2017
Department of Statistical Science Duke University FIRST YEAR EXAM - SPRING 017 Monday May 8th 017, 9:00 AM 1:00 PM NOTES: PLEASE READ CAREFULLY BEFORE BEGINNING EXAM! 1. Do not write solutions on the exam;
More informationTamsui Oxford Journal of Information and Mathematical Sciences 29(2) (2013) Aletheia University
Tamsui Oxford Journal of Information and Mathematical Sciences 292 2013 219-238 Aletheia University Relations for Marginal and Joint Moment Generating Functions of Extended Type I Generalized Logistic
More informationfix- gx x +0 ff x 0 and fgx- gfxl 2x" 0 if x 0 so that f and g are compatible on R with the usual metric.
Internat. J. Math. & Math. Sci. VOL. Ii NO. 2 (1988) 285-288 285 COMPATIBLE MAPPINGS AND COMMON FIXED POINTS (2) GERALD JUNGCK Department of Mathematics Bradley University Peoria, Illinois 61625 (Received
More informationPARAMETER ESTIMATION FOR THE LOG-LOGISTIC DISTRIBUTION BASED ON ORDER STATISTICS
PARAMETER ESTIMATION FOR THE LOG-LOGISTIC DISTRIBUTION BASED ON ORDER STATISTICS Authors: Mohammad Ahsanullah Department of Management Sciences, Rider University, New Jersey, USA ahsan@rider.edu) Ayman
More informationOn a six-parameter generalized Burr XII distribution
On a six-parameter generalized Burr XII distribution arxiv:0806.1579v1 [math.st] 10 Jun 2008 A.K. Olapade Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria. E-mail: akolapad@oauife.edu.ng
More informationarxiv: v2 [nlin.cd] 17 Aug 2010
Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas. Diego F. M. Oliveira arxiv:1008.1344v2 [nlin.cd] 17 Aug 2010 Max Planck Institute for Dynamics and Self-Organization
More informationThis article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
More informationJordan Journal of Mathematics and Statistics (JJMS) 7(4), 2014, pp
Jordan Journal of Mathematics and Statistics (JJMS) 7(4), 2014, pp.257-271 ON RELATIONS FOR THE MOMENT GENERATING FUNCTIONS FROM THE EXTENDED TYPE II GENERALIZED LOGISTIC DISTRIBUTION BASED ON K-TH UPPER
More informationMODULI SPACE OF FILTERED λ-ring STRUCTURES OVER A FILTERED RING
IJMMS 2004:39, 2065 2084 PII. S0161171204304138 http://ijmms.hindawi.com Hindawi Publishing Corp. MODULI SPACE OF FILTERED λ-ring STRUCTURES OVER A FILTERED RING DONALD YAU Received 10 April 2003 Motivated
More informationOn the Comparison of Fisher Information of the Weibull and GE Distributions
On the Comparison of Fisher Information of the Weibull and GE Distributions Rameshwar D. Gupta Debasis Kundu Abstract In this paper we consider the Fisher information matrices of the generalized exponential
More informationMaximum Likelihood and Bayes Estimations under Generalized Order Statistics from Generalized Exponential Distribution
Applied Mathematical Sciences, Vol. 6, 2012, no. 49, 2431-2444 Maximum Likelihood and Bayes Estimations under Generalized Order Statistics from Generalized Exponential Distribution Saieed F. Ateya Mathematics
More informationCOEFFICIENTS OF SINGULARITIES OF THE BIHARMONIC PROBLEM OF NEUMANN TYPE: CASE OF THE CRACK
IJMMS 23:5, 35 313 PII. S161171231278X http://ijmms.hindawi.com Hindawi Publishing Corp. COEFFICIENTS OF SINGULARITIES OF THE BIHARMONIC PROBLEM OF NEUMANN TYPE: CASE OF THE CRACK WIDED CHIKOUCHE and AISSA
More informationOptimum Workforce Scheduling Under the (14, 21) Days-Off Timetable
JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, 6(3), 191 199 Copyright c 00, Lawrence Erlbaum Associates, Inc. Optimum Workforce Scheduling Under the (14, 1) Days-Off Timetable HESHAM K. ALFARES
More informationTwo Weighted Distributions Generated by Exponential Distribution
Journal of Mathematical Extension Vol. 9, No. 1, (2015), 1-12 ISSN: 1735-8299 URL: http://www.ijmex.com Two Weighted Distributions Generated by Exponential Distribution A. Mahdavi Vali-e-Asr University
More informationASM Study Manual for Exam P, Second Edition By Dr. Krzysztof M. Ostaszewski, FSA, CFA, MAAA Errata
ASM Study Manual for Exam P, Second Edition By Dr. Krzysztof M. Ostaszewski, FSA, CFA, MAAA (krzysio@krzysio.net) Errata Effective July 5, 3, only the latest edition of this manual will have its errata
More information