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 BhattiGeneralized Family of Estimators for Imputing Scrambled Responses
http://jirss.irstat.ir/browse.php?a_id=441&sid=1&slc_lang=en
<p>When there is a high correlation between the study and the auxiliary variables, the rank of the auxiliary variable also correlates with the study variable. Then, the use of the rank as an additional auxiliary variable may be helpful to increase the efficiency of the estimator of the mean or total of the population. In the present study, we propose two generalized families of estimators for imputing scrambling response by using the variance and rank of the auxiliary variable. Expressions for bias and mean squared error are obtained up to the first order of approximation. A numerical study is carried out to observe the performance of estimators. </p>
Sohail Umar SohailImproved Cramer-Rao Inequality for Randomly Censored Data
http://jirss.irstat.ir/browse.php?a_id=472&sid=1&slc_lang=en
As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censored data.BLS PrakasaraoSpatial Interpolation Using Copula for non-Gaussian Modeling of Rainfall Data
http://jirss.irstat.ir/browse.php?a_id=462&sid=1&slc_lang=en
‎One of the most useful tools for handling multivariate distributions of dependent variables in terms of their marginal distribution is a copula function‎. ‎The copula families captured a fair amount of attention due to their applicability and flexibility in describing the non-Gaussian spatial dependent data‎. ‎The particular properties of the spatial copula are rarely seen in all the known copula families‎. ‎In the present paper‎, ‎based on the weighted geometric mean of two Max-id copulas family‎, ‎the spatial copula function is provided‎. ‎Afterwards‎, ‎the proposed copula‎, ‎along with the Bees algorithm is used to explore the spatial dependency and to interpolate the rainfall data in Iran's Khuzestan province‎. Mehdi OmidiRidge stochastic restricted estimators in semiparametric linear measurement error models
http://jirss.irstat.ir/browse.php?a_id=442&sid=1&slc_lang=en
<p>In this article we consider the stochastic restricted ridge estimation in semipara-<br>
metric linear models when the covariates are measured with additive errors. The<br>
development of penalized corrected likelihood method in such model is the ba-<br>
sis for derivation of ridge estimates. The asymptotic normality of the resulting<br>
estimates are established. Also, necessary and sufficient conditions, for the su-<br>
periority of the proposed estimator over its counterpart, for selecting the ridge<br>
parameter k are obtained. A Monte Carlo simulation study is also performed<br>
to illustrate the finite sample performance of the proposed procedures. Finally<br>
theoretical results are applied to Egyptian pottery Industry data set.</p>
Hadi EmamiGeneralized Baum-Welch and Viterbi Algorithms Based on the Direct Dependency among Observations
http://jirss.irstat.ir/browse.php?a_id=434&sid=1&slc_lang=en
<p style="margin: 0px;">‎The parameters of a Hidden Markov Model (HMM) are transition and emission probabilities‎. ‎Both can be estimated using the Baum-Welch algorithm‎. ‎The process of discovering the sequence of hidden states‎, ‎given the sequence of observations‎, ‎is performed by the Viterbi algorithm‎. ‎In both Baum-Welch and Viterbi algorithms‎, ‎it is assumed that given the states‎, ‎the observations are independent from each other‎. ‎‎In this paper‎, ‎we first consider the direct dependency between consecutive observations in HMM‎, ‎and then use conditional independence relations in the context of a Bayesian network which is a probabilistic graphical model for generalizing the Baum-Welch and Viterbi algorithms‎. ‎We compare the performance of the generalized algorithms with the commonly used ones in simulation studies for synthetic data‎. ‎We finally apply these algorithms on real datasets which are related to biological and inflation data‎. ‎We show that the generalized Baum-Welch and Viterbi algorithms significantly outperform the conventional ones when the sample sizes become larger‎.</p>
Vahid Rezaei TabarNonlinear Regression Models Based on Slash Skew-elliptical Errors
http://jirss.irstat.ir/browse.php?a_id=389&sid=1&slc_lang=en
<p style="margin: 0px;">In this paper‎, ‎the‎ ‎nonlinear regression models when the model errors follow a slash‎ ‎skew-elliptical distribution‎, ‎are considered‎. ‎In the special case‎ ‎of nonlinear regression models under slash skew-t distribution‎, ‎we‎ ‎present some distributional properties‎, ‎and to estimate their‎ ‎parameters‎, ‎we use an EM-type algorithm‎. ‎Also‎, ‎to find the‎ ‎estimation errors‎, ‎we derive the observed information matrix‎ ‎analytically‎. ‎To describe the influence of the observations on the‎</p>
<p style="margin: 0px;">‎ML estimates‎, ‎we use a sensitivity analysis‎. ‎Finally‎, ‎we conduct‎ ‎some simulation studies and a real data analysis to show the‎ ‎performance of the proposed model‎. ‎</p>
Rahman FarnooshOptimal Allocation of Policy Layers for Exponential Risks
http://jirss.irstat.ir/browse.php?a_id=474&sid=1&slc_lang=en
‎In this paper‎, ‎we study the problem of optimal allocation of insurance layers for a portfolio of i.i.d exponential risks‎. ‎Using the first stochastic dominance criterion‎, ‎we obtain an optimal allocation for the total retain risks faced by a policyholder‎. ‎This result partially generalizes the known result in the literature for deductible as well as policy limit coverages‎. Muhyiddin Izadi