Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
9
2
2013
3
1
A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test
115
131
FA
S.
Baratpour
baratpour@um.ac.ir
F.
Khodadadi
ne_khodadad2@yahoo.com
10.18869/acadpub.jsri.9.2.115
Rayleigh distribution is widely used for life-time modeling and is important in electro vacuum devices and communication engineering. Rao et al. (2004) suggested the Cumulative Residual Entropy (CRE), which is the extension of the Shannon entropy to the the cumulative distribution function. In this paper, a general class of maximum CRE distributions is introduced and then we characterize the Rayleigh distribution and use it to construct a goodness-of-fit test for ascertaining appropriateness of such model. For constructing the test statistics, we use Cumulative residual Kullback-Leibler information (CKL) that was introduced by Baratpour and Habibi (2012). Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for the test statistics. A Monte Carlo power analysis is performed for various alternatives and sample sizes in order to compare the proposed test with several existing goodness-of-fit tests based on the empirical distribution. We find that the proposed test has good power properties. The use of the proposed test is shown in an illustrative example.
Cumulative residual entropy, maximum entropy, Kullback-Leibler divergence, Rayleigh distribution, goodness of fit, power study
http://jsri.srtc.ac.ir/article-1-203-en.html
http://jsri.srtc.ac.ir/article-1-203-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
9
2
2013
3
1
Parametric Empirical Bayes Test and Its Application to Selection of Wavelet Threshold
133
146
EN
Mona
Shokripour
m_shokripour@sbu.ac.ir
Adel
Mohammadpour
adel@aut.ac.ir
Mina
Aminghafari
aminghafari@aut.ac.ir
10.18869/acadpub.jsri.9.2.133
In this article, we propose a new method for selecting level dependent threshold in wavelet shrinkage using the empirical Bayes framework. We employ both Bayesian and frequentist testing hypothesis instead of point estimation method. The best test yields the best prior and hence the more appropriate wavelet thresholds. The standard model functions are used to illustrate the performance of the proposed method and make comparisons with other traditional methods.
Bayes test, parametric empirical Bayes, most powerful test, heavy tailed distribution, unbiased test, wavelet thresholding
http://jsri.srtc.ac.ir/article-1-60-en.html
http://jsri.srtc.ac.ir/article-1-60-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
9
2
2013
3
1
Some Results on a Generalized Archimedean Family of Copulas
147
158
EN
Ali
Dolati
adolati@yazd.ac.ir
Mojdeh
Karbasian
mkarbasian9@gmail.com
10.18869/acadpub.jsri.9.2.147
Durante et al. (2007) introduced a class of bivariate copulas depending on two generators which generalizes some known families such as the Archimedean copulas. In this paper we provide some result on properties of this family when the generators are certain univariate survival functions.
Copula, Archimedean copula, dependence ordering, survival function
http://jsri.srtc.ac.ir/article-1-61-en.html
http://jsri.srtc.ac.ir/article-1-61-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
9
2
2013
3
1
Some Improvment in the Estimation of Population Mean in Cluster Sampling
159
177
EN
M.
Sakizadeh
mansoure6611@yahoo.com
A.
Gerami
agerami@ut.ac.ir
10.18869/acadpub.jsri.9.2.159
Gupta and Shabbir (2008) have suggested an alternative form of ratio-type estimator for estimating the population mean. In this paper, we introduced new estimators by mixing two, stratified and cluster sampling method. Then we improved these estimators by using auxiliary variables and introducing new estimators. For sampling in infinite populations with a high geographic dispersion, the population will be divided into some smaller sub-population which leads to dispersion reduction to some extent. This will affect the variance of the estimator. Additionally dividing the population will result in saving cost, time and eases calculations.
Auxiliary variables, cluster sampling, estimator, stratified sampling.
http://jsri.srtc.ac.ir/article-1-62-en.html
http://jsri.srtc.ac.ir/article-1-62-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
9
2
2013
3
1
Model Confidence Set Based on Kullback-Leibler Divergence Distance
179
193
EN
G.
Barmalzan
ghbarmalzan@uoz.ac.ir
T.
Payandeh Najafabad
amirtpayandeh@sbu.ac.ir
10.18869/acadpub.jsri.9.2.179
Consider the problem of estimating true density, h(.) based upon a random sample X1,…, Xn. In general, h(.)is approximated using an appropriate in some sense, see below) model fƟ(x). This article using Vuongchr('39')s (1989) test along with a collection of k(> 2) non-nested models constructs a set of appropriate models, say model confidence set, for unknown model h(.).Application of such confidence set has been confirmed through a simulation study.
Kullback-Leibler divergence distance, confidence set, model selection, non-nested models, Vuong's test.
http://jsri.srtc.ac.ir/article-1-63-en.html
http://jsri.srtc.ac.ir/article-1-63-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
9
2
2013
3
1
Estimation for the Type-II Extreme Value Distribution Based on Progressive Type-II Censoring
195
221
EN
K.
Ahmadi
K.Ahmadi@birgand.ac.ir
V.
Ahrari Khalaf
v_ahrary84@yahoo.com
M.
Rezaei
Mjrezaei@yahoo.com
10.18869/acadpub.jsri.9.2.195
In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes estimates using both the symmetric and asymmetric loss functions via squared error loss, LINEX loss, and general entropy loss functions. Bayes estimates are obtained using the idea of Lindley and Markov chain Monte Carlo techniques. Finally, Monte Carlo simulations are presented to illustrate the methods discussed in this paper. Analysis is also carried out for a real data set.
Approximate maximum likelihood estimators, Bayes estimates, EM algorithm, Lindley's approximation, Monte Carlo simulation, progressive type-II censoring.
http://jsri.srtc.ac.ir/article-1-64-en.html
http://jsri.srtc.ac.ir/article-1-64-en.pdf