Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
10
1
2013
9
1
Efficient Estimation of the Density and Cumulative Distribution Function of the Generalized Rayleigh Distribution
1
22
EN
M.
Alizadeh
alizadeh_mojtaba_san@yahoo.com
F.
Bagheri
f_bagheri@sbu.ac.ir
M.
M. Khaleghy Moghaddam
m.khaleghi@sanru.ac.ir
10.18869/acadpub.jsri.10.1.1
The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modeling general lifetime data. It has been shown that MLE is better than UMVUE and UMVUE is better than the others. An application to waiting times (min) of 100 bank customers
Generalized Rayleigh distribution, maximum likelihood estimator, uniformly minimum variance unbiased estimator, percentile estimator, least squares estimator, weighted least squares estimator
http://jsri.srtc.ac.ir/article-1-53-en.html
http://jsri.srtc.ac.ir/article-1-53-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
10
1
2013
9
1
Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization
23
39
EN
Devendra
Kumar
devendrastats@gmail.com
10.18869/acadpub.jsri.10.1.23
Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.
Generalized order statistics, order statistics, record values, generalized Pareto distribution, recurrence relations, conditional expectation and characterization
http://jsri.srtc.ac.ir/article-1-52-en.html
http://jsri.srtc.ac.ir/article-1-52-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
10
1
2013
9
1
Analysis of Record Data from the Scaled Logistic Distribution
41
62
EN
A.
Asgharzadeh
a.asgharzadeh@umz.ac.ir
M.
Abdi
meabdi.z@gmail.com
R.
valiollahi
valiollahi.reza@gmail.com
10.18869/acadpub.jsri.10.1.41
In this paper, we consider the estimation of the unknown parameter of the scaled logistic distribution on the basis of record values. The maximum likelihood method does not provide an explicit estimator for the scale parameter. In this article, we present a simple method of deriving an explicit estimator by approximating the likelihood function. Bayes estimator is obtained using importance sampling. Asymptotic confidence intervals, bootstrap confidence interval and credible interval are also proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of one real data set is also given for illustrative purposes.
Bayes estimation, maximum likelihood estimation, Monte Carlo simulation, record values, importance sampling
http://jsri.srtc.ac.ir/article-1-54-en.html
http://jsri.srtc.ac.ir/article-1-54-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
10
1
2013
9
1
Plain Answers to Several Questions about Association/Independence Structure in Complete/Incomplete Contingency Tables
63
84
EN
K.
Ghoreishi
atty_ghoreishi@yahoo.com
R.
Meshkani
mrmeshkani@gmail.com
10.18869/acadpub.jsri.10.1.63
In this paper, we develop some results based on Relational model (Klimova, et al. 2012) which permits a decomposition of logarithm of expected cell frequencies under a log-linear type model. These results imply plain answers to several questions in the context of analyzing of contingency tables. Moreover, determination of design matrix and hypothesis-induced matrix of the model will be discussed. Properties of maximum likelihood estimators of the model parameters are obtained. Some new model residuals and an alternative symmetric chi-square criterion are given. Two real examples illustrate the method.
Association models, Context Specific models, Graphical models, Log-linear models, Relational models
http://jsri.srtc.ac.ir/article-1-55-en.html
http://jsri.srtc.ac.ir/article-1-55-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
10
1
2013
9
1
Exp-Uniform Distribution: Properties and Characterizations
85
106
EN
Z.
Javanshiri
zo_ja15@um.ac.ir
A.
Habibi Rad
ahabibi@um.ac.ir
H.
G. Hamedani
g.hamedani@mu.edu
10.18869/acadpub.jsri.10.1.85
In this paper, we study properties of exp-uniform distribution and its applications. We provide closed forms for the density function and moments of order statistics and we also discuss estimation of the parameters via the maximum likelihood method. We will present certain characterizations of exp-uniform distribution. The applications of this distribution are illustrated by fitting it to three real data sets and comparing the results with other lifetime distributions. We hope that this distribution will attract wider applications in lifetime models.
Characterizations, maximum likelihood estimator, order statistics
http://jsri.srtc.ac.ir/article-1-56-en.html
http://jsri.srtc.ac.ir/article-1-56-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
10
1
2013
9
1
A Brief Determination of Certain Class of Power Semicircle Distribution
107
111
EN
Rasool
Roozegar
rroozegar@yazd.ac
Reza
Soltani
soltani@kuc01.kuniv.edu.kw
10.18869/acadpub.jsri.10.1.107
In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gauss-hypergeometric function unlike the long proof in Roozegar and Soltani (2013).
Power semicircle distribution, Gauss-hypergeometric function, randomly weighted average, arcsine distribution
http://jsri.srtc.ac.ir/article-1-57-en.html
http://jsri.srtc.ac.ir/article-1-57-en.pdf