Journal of the Iranian Statistical Society
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Journal of The Iranian Statistical Society - Journal articles for year 2018, Volume 17, Number 2Yektaweb Collection - https://yektaweb.comen2018/4/12A 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 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>
Muhammad Umair 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-metric linear models when the covariates are measured with additive errors. The development of penalized corrected likelihood method in such model is the basis for derivation of ridge estimates. The asymptotic normality of the resulting estimates are established. Also, necessary and sufficient conditions, for the superiority of the proposed estimator over its counterpart, for selecting the ridge parameter k are obtained. A Monte Carlo simulation study is also performed to illustrate the finite sample performance of the proposed procedures. Finally 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 IzadiAsymmetric Uniform-Laplace distribution: Properties and Applications
http://jirss.irstat.ir/browse.php?a_id=438&sid=1&slc_lang=en
<p style="margin: 0px;">‎The goal of this study is to introduce an Asymmetric Uniform-Laplace (AUL) distribution‎. ‎We present a detailed theoretical description of this distribution‎. ‎We try to estimate the parameters of AUL distribution using maximum likelihood method‎. ‎Since the likelihood approach results in complicated forms‎, ‎we suggested a bootstrap-based approach for estimating the parameters‎. ‎The proposed method is mainly based on the shape of the empirical density‎.</p>
<p style="margin: 0px;">‎We conduct a simulation study to assess the performance of the proposed procedure‎. ‎We also fit the AUL distribution to real datasets‎: ‎daily working time and Pontius datasets‎. ‎The results show that AUL distribution is the more appropriate choice than the Skew-Normal‎, ‎Skew t‎, ‎Asymmetric Laplace and Uniform-Normal distributions.</p>
Rahim MahmoudvandCorrected Confidence Intervals for a Small Area Parameter through the Weighted Estimator under the Basic Area Level Model
http://jirss.irstat.ir/browse.php?a_id=440&sid=1&slc_lang=en
<p>Area level linear mixed models can be generally applied to produce small area indirect estimators when only aggregated data such as sample means are available‎. ‎This paper tries to fill an important research gap in small area estimation literature‎, ‎the problem of constructing confidence intervals (CIs) when the estimated variance of the random effect as well as the estimated mean squared error (MSE) are negative‎. ‎More precisely‎, ‎the coverage accuracy of the proposed CI is of the order O<sup>-3/2</sup>‎, ‎where $m$ is the number of sampled areas‎. ‎The performance of the proposed method is illustrated with respect to coverage probability (CP) and average length (AL) using a simulation experiment‎. ‎Simulation results demonstrate the superiority of the proposed method over existing naive CIs‎. ‎In addition‎, ‎the proposed CI based on the weighted estimator is comparable with the existing corrected CIs based on empirical best linear unbiased predictor (EBLUP) in the literature‎.</p>
Yegnanew ShiferawStochastic Models for Pricing Weather Derivatives using Constant Risk Premium
http://jirss.irstat.ir/browse.php?a_id=465&sid=1&slc_lang=en
<p style="margin: 0px;">‎Pricing weather derivatives is becoming increasingly useful‎, ‎especially in developing economies‎. ‎We describe a statistical model based approach for pricing weather derivatives by modeling and forecasting daily average temperatures data which exhibits long-range dependence‎. ‎We pre-process the temperature data by filtering for seasonality and volatility and fit autoregressive fractionally integrated moving average (ARFIMA) models‎, ‎employing the preconditioned conjugate gradient (PCG) algorithm for fast computation of the likelihood function‎. ‎We illustrate our approach using daily temperatures data from 1970 to 2008 for cities traded on the Chicago Mercantile Exchange (CME)‎, ‎which we employ for pricing degree days futures contracts‎. ‎We compare the statistical approach with traditional burn analysis using a simple additive risk loading principle for pricing‎, ‎where‎ ‎the risk premium is estimated by the method of least squares using data on observed prices and the corresponding estimate of prices from the best model we fit to the temperatures data.</p>
Nalini RavishankerOn the Preliminary Test Generalized Liu Estimator with Series of Stochastic Restrictions
http://jirss.irstat.ir/browse.php?a_id=486&sid=1&slc_lang=en
‎When series of stochastic restrictions are available‎, ‎we study the performance of the preliminary test generalized Liu estimators (PTGLEs) based on the Wald‎, ‎likelihood ratio and lagrangian multiplier tests‎. ‎In this respect‎, ‎the optimal range of biasing parameter is obtained under mean square error sense‎. ‎For this‎, ‎the minimum/maximum value of the biasing matrix components is used to give the proper optimal range‎, ‎where the biasing matrix is D=diag(d<sub>1</sub>,d<sub>2</sub>,...,d<sub>p</sub>)‎, 0<<d<sub>i<1‎, i=1,...,p‎. ‎We support out findings by some numerical illustrations‎.</d<sub>Seyed Moahammad M. Tabatabaey