Journal of the Iranian Statistical Society
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Journal of The Iranian Statistical Society - Journal articles for year 2017, Volume 18, Number 1Yektaweb Collection - http://www.yektaweb.comen2017/10/9A New Method For Generating Continuous Bivariate Families
http://jirss.irstat.ir/browse.php?a_id=289&sid=1&slc_lang=en
<p style="margin: 0px;">‎Recently‎, ‎it has been observed that a new method for generating the continuous distributions‎, ‎T-X family‎, ‎can be quite effectively used‎ ‎to analyze the data in one dimension‎. ‎The aim of this study‎ ‎was to generalize this method to the two dimensional space so that the marginals would have the‎ ‎T-X distributions‎. ‎In doing so‎, ‎several examples and properties of this family‎ ‎have been presented‎. ‎As an application‎, ‎a special distribution of this family‎, ‎called bivariate Weibull-Rayleigh-Rayleigh‎, ‎was fitted to one data set and showed a better indexes fit‎. </p>
Hossein BevraniShrinkage Estimation in Restricted Elliptical Regression Model
http://jirss.irstat.ir/browse.php?a_id=439&sid=1&slc_lang=en
<p style="margin: 0px;">‎In the restricted elliptical linear model‎, ‎an approximation for the risk of a general shrinkage estimator of‎</p>
<p style="margin: 0px;">‎a general shrinkage estimator of regression vector-parameter is given‎. ‎superiority condition of the‎</p>
<p style="margin: 0px;">‎shrinkage estimator over the restricted estimator is investigated‎, ‎under elliptical assumption‎. ‎It is evident from the numerical results that the shrinkage estimator performs better than the unrestricted one‎, ‎in the multivariate t-regression model‎.</p>
Reza Falah Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure
http://jirss.irstat.ir/browse.php?a_id=415&sid=1&slc_lang=en
<p>In this paper‎, ‎borrowing the intuition in Rao et al‎. ‎(2004)‎, ‎we introduce a cumulative version of inaccuracy measure (CIM)‎. ‎Also we obtain interesting and applicable properties of CIM for different cases based on residual‎, ‎past and interval lifetime random variables‎. ‎Relying on various application of stochastic classes in reliability and information theory field‎, ‎we study new classes of lifetime in terms of CIM along with their relations with other famous ageing classes‎. ‎Furthermore‎, ‎some characterization results are obtained under proportional reversed hazard rate model‎. ‎Finally‎ ‎an extension of CIM‎, ‎considering the time t changes in a range (t<sub>1</sub>,t<sub>2</sub>) called the interval cumulative residual (past) inaccuracy (ICR(P)I) is derived‎. ‎We investigate ICRI's relation with its analogous version based on Shannon entropy‎. </p>
Mohammad KhorashadizadehBayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function
http://jirss.irstat.ir/browse.php?a_id=395&sid=1&slc_lang=en
<p style="margin: 0px;"><span class="fontstyle0">In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfolio. When the prior knowledge is vague, the E-Bayesian and robust Bayesian analysis can be used to handle the uncertainty in specifying the prior distribution by considering a class of priors instead of a single prior. In this paper, we study the E-Bayes and robust Bayes premium estimation and prediction in exponential model under the squared log error loss function. A prequential analysis in a simulation study is carried out to compare the proposed predictors. Finally, a real data example is included for illustrating the results.</span></p>
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Azadeh KiapourModel Selection Based on Tracking Interval under Unified Hybrid Censored Samples
http://jirss.irstat.ir/browse.php?a_id=382&sid=1&slc_lang=en
<p><span class="fontstyle0">The aim of statistical modeling is to identify the model that most closely approximates the underlying process. Akaike information criterion (AIC) is commonly used for model selection but the precise value of AIC has no direct interpretation. In this paper we use a normalization of a di</span><span class="fontstyle2">ff</span><span class="fontstyle0">erence of Akaike criteria in comparing between the two rival models under unified hybrid censoring scheme. Asymptotic properties of maximum likelihood estimator based on the missing information principle are derived. Also, asymptotic distribution of the normalized di</span><span class="fontstyle2">ff</span><span class="fontstyle0">erence of AIC’s is obtained and it is used to construct an interval, called tracking interval, for comparing the two competing models. Monte Carlo simulations are performed to examine how the proposed interval works for di</span><span class="fontstyle2">ff</span><span class="fontstyle0">erent censoring schemes. Two real data sets have been analyzed for illustrative purposes. The first is selecting between Weibull<br>
and generalized exponential distributions for main component of spearmint essential oil purification data. The second is the choice between models of the lifetimes of 20 electronic components.</span><br style="line-height: normal; text-align: -webkit-auto; text-size-adjust: auto;" >
</p>
Hanieh PanahiA New Distribution Family Constructed by Fractional Polynomial Rank Transmutation
http://jirss.irstat.ir/browse.php?a_id=444&sid=1&slc_lang=en
<p style="margin: 0px;">In this study‎, ‎a new polynomial rank transmutation is proposed with the help of‎ ‎ the idea of quadratic rank transmutation mapping (QRTM)‎. ‎This polynomial rank‎ ‎ transmutation is allowed to extend the range of the transmutation parameter from‎ ‎ [-1,1] to [-1,k]‎. ‎At this point‎, ‎the generated distributions gain more‎ ‎ flexibility than a transmuted distribution constructed by QRTM‎. ‎The distribution family obtained in this transmutation is considered‎ ‎ to be an alternative to the distribution families obtained by quadratic rank‎ ‎ transmutation‎. ‎Statistical and reliability properties of this family are‎ ‎ examined‎. ‎Considering Weibull distribution as the base distribution‎, ‎the‎ ‎ importance and the flexibility of the proposed families are illustrated by two‎ ‎ applications‎. ‎</p>
Mehmet YilmazOn Bivariate Generalized Exponential-Power Series Class of Distributions
http://jirss.irstat.ir/browse.php?a_id=422&sid=1&slc_lang=en
<p style="margin: 0px;">‎In this paper‎, ‎we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions‎.</p>
<p style="margin: 0px;">‎This new class contains the bivariate generalized exponential-Poisson‎, ‎bivariate generalized exponential-logarithmic‎, ‎bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as special‎ ‎cases‎. ‎We derive different properties of the proposed class of distributions‎. ‎It is observed that the proposed class of‎ ‎bivariate distributions is a very flexible class of distribution functions‎. ‎The joint probability density functions can have‎ ‎variety of shapes‎. ‎It can be bimodal as well as heavy tail also‎. ‎This distribution has five parameters‎. ‎The maximum likelihood‎ ‎estimators of the parameters cannot be obtained in closed form‎. ‎We propose to use EM algorithm to compute the maximum‎ ‎likelihood estimators of the unknown parameters‎. ‎It is observed that the proposed EM algorithm can be implemented very‎ ‎easily in practice‎. ‎One data set has been analyzed for illustrative purposes‎. ‎It is observed that‎ ‎the proposed model and the EM algorithm work quite well in practice‎.</p>
Rasool RoozegarOn Modified Log Burr XII Distribution
http://jirss.irstat.ir/browse.php?a_id=429&sid=1&slc_lang=en
<p dir="ltr" style="margin: 0px;"> In this paper‎, ‎we present a‎ ‎Modified Log Burr XII (MLBXII) distribution developed on the basis‎ ‎of a generalized log Pearson differential equation‎. ‎This‎ ‎distribution is also obtained from compounding mixture of‎ ‎distributions‎. ‎Moments‎, ‎inequality measures‎, ‎uncertainty measures‎ ‎and reliability measures are theoretically established‎. ‎Characterizations of MLBXII distribution are also studied via‎ ‎different techniques‎. ‎Parameters of MLBXII distribution are‎ ‎estimated using maximum likelihood method‎. ‎Goodness of fit of this‎ ‎distribution through different methods is studied.</p>
Fiaz Ahmad Bhatti