Journal of the Iranian Statistical Society
http://jirss@irstat.ir
Journal of The Iranian Statistical Society - Journal articles for year 2017, Volume 17, Number 0Yektaweb Collection - http://www.yektaweb.comen2017/12/10Some 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;">In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the</p>
<p style="margin: 0px;">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.</p>
<p></p>
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>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 difference 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 difference of AIC’s is obtained and it is used to construct an interval‎, ‎say tracking interval‎, ‎for comparing the two competing models‎. ‎Monte Carlo simulations are performed to examine how the proposed interval works for different censoring scheme‎. ‎Two real datasets have been analyzed for illustrative purposes‎. ‎The first is selecting between Weibull 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.</p>
Hanieh PanahiOn Concomitants of Order Statistics from Farlie-Gumbel-Morgenstern Bivariate Lomax Distribution and its Application in Estimation
http://jirss.irstat.ir/browse.php?a_id=303&sid=1&slc_lang=en
<p>‎In this paper‎, ‎we have dealt with the distribution theory of concomitants of order statistics arising from Farlie-Gumbel-Morgenstern bivariate Lomax distribution‎. ‎We have discussed the estimation of the parameters associated with the distribution of the variable Y of primary interest‎, ‎based on the ranked set sample defined by ordering the marginal observations on an auxiliary variable X‎, ‎when (X,Y) follows a Farlie-Gumbel-Morgenstern bivariate Lomax distribution‎. ‎When the association parameter and the shape parameter corresponding to $Y$ are known‎, ‎we have proposed four estimators‎, ‎viz.‎, ‎an unbiased estimator based on the Stokes' ranked set sample‎, ‎the best linear unbiased estimator based on the Stokes' ranked set sample‎, ‎the best linear unbiased estimator based on the extreme ranked set sample and the best linear unbiased estimator based on the multistage extreme ranked set sample for the scale parameter of the variable of primary interest‎. ‎The relative efficiencies of these estimators have also been worked out‎.</p>
Anne PhilipTwo-step Smoothing Estimation of the Time-variant Parameter with Application to Temperature Data
http://jirss.irstat.ir/browse.php?a_id=348&sid=1&slc_lang=en
<p>‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameters of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time points and then compute the final estimator at any time by smoothing the raw estimators‎. ‎We will call these estimators two-step local polynomial smoothing estimator and two-step kernel smoothing estimator‎. ‎We derive these two two-step smoothing estimators by modeling raw estimates of the time-variant parameter from any regression model or probability model and then establish a mathematical relationship between these two estimators‎. ‎Our two-step estimation method is applied to temperature data from Dhaka‎, ‎the capital city of Bangladesh‎. ‎Extensive simulation studies under different cross-sectional and longitudinal frameworks have been conducted to check the finite sample MSE of our estimators‎. ‎Narrower bootstrap confidence bands and smaller MSEs from application and simulation results show the superiority of the local polynomial smoothing estimator over the kernel smoothing estimator‎. </p>
Mohammed ChowdhuryPrediction for Lindley Distribution Based on Type-II Right Censored Samples
http://jirss.irstat.ir/browse.php?a_id=358&sid=1&slc_lang=en
<p>‎Lindley distribution has received a considerable attention in the statistical literature due to its simplicity‎. ‎In this paper‎, ‎we consider the problem of predicting the failure times of experimental units that are censored in a right-censored experiment when the underlying lifetime is Lindley distributed‎. ‎The maximum likelihood predictor‎, ‎the best unbiased predictor and the conditional median predictor are derived‎. ‎Prediction intervals based on these predictors are considered‎. ‎We further propose two resampling-based procedures for obtaining the prediction intervals‎. ‎A numerical example is used to illustrate the methodology developed in this paper‎. ‎Finally‎, ‎a Monte Carlo simulation study is employed to evaluate the performance of different prediction methods‎.</p>
Akbar AsgharzadehImproved estimation in Rayleigh type-II censored data under a bounded loss utilizing a point guess value
http://jirss.irstat.ir/browse.php?a_id=388&sid=1&slc_lang=en
<p>‎The problem of shrinkage testimation for the Rayleigh scale‎ ‎parameter θ based on censored samples under the reflected‎ ‎gamma loss function is considered‎. We obtain the minimum risk‎ ‎estimator among a subclass and compute its risk‎. ‎A shrinkage‎ ‎testimator based on acceptance or rejection of a null hypothesis‎ <span class="fontstyle2">H</span><span class="fontstyle3">0 </span><span class="fontstyle0">: </span><span class="fontstyle2">θ </span><span class="fontstyle0">= </span><span class="fontstyle2">θ</span><span class="fontstyle3">0</span> is constructed‎, ‎where <span class="fontstyle2">θ</span><span class="fontstyle3">0</span> is a point‎ ‎guess value of θ‎. ‎The risk of the proposed shrinkage‎ ‎testimator is computed numerically and compared with the minimum‎ ‎risk estimator‎. ‎One data set is analyzed for illustrative‎ ‎purposes‎. </p>
Mehran Naghizadeh QomiSome Results on Weighted Cumulative Entropy
http://jirss.irstat.ir/browse.php?a_id=380&sid=1&slc_lang=en
<p>Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009)‎, ‎<span class="fontstyle0">Misagh et al. (2011)</span></p>
<p>proposed a weighted information that is based on cumulative entropy which is called "weighted cumulative entropy'' (WCE)‎. ‎The above-mentioned model is a "Shift-dependent uncertainty measure''‎. ‎In this paper‎, ‎we examine some of the properties of WCE and obtain some bounds for it‎. ‎In order to estimate this information measure‎, ‎we put forward empirical WCE‎. ‎Furthermore‎, ‎in some theorems we have some characterization results‎. ‎We explore that if the WCE of first (last) order statistics are equal for two distributions‎, ‎then this two distributions will be equal‎. </p>
Malihe MiraliA 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 BevraniSkew Laplace Finite Mixture modelling
http://jirss.irstat.ir/browse.php?a_id=409&sid=1&slc_lang=en
<p></p>
<div dir="ltr" font-size:="" id="m_-892245609597034382yui_3_16_0_ym19_1_1492992463992_5365" new="" style="color: rgb(0, 0, 0); font-family: " times="">
<p style="margin: 0px;">‎This paper presents a new mixture model via considering the univariate skew Laplace distribution‎. ‎The new model can handle both heavy tails and skewness and is multimodal‎. ‎Describing some properties of the proposed model‎, ‎we present a feasible EM algorithm for iteratively‎ ‎computing maximum likelihood estimates‎. ‎We also derive the observed information matrix for obtaining‎ ‎the asymptotic standard errors of parameter estimates‎. ‎The finite sample properties of the obtained estimators‎ ‎together with the consistency of the associated standard error of parameter estimates are investigated by a‎ ‎simulation study‎. ‎We also demonstrate the flexibility and usefulness of the new model by analyzing real data‎ ‎example‎. </p>
</div>
Mehrdad NaderiShrinkage 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