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Samira Nayeban, Abdol Hamid Rezaei Roknabadi, Gholam Reza Mohtashami Borzadaran,
Volume 7, Issue 2 (3-2014)
Abstract
In this paper, first the Bhattacharray and Kshirsagar bounds are introduced and then the multiparameter Bhattacharyya bound is presented in simpler and understandable form. Furthermore, the multiparameter Kshirsagar lower bound, which has not been studied yet, is obtained. Finally, by presenting some example of Log-normal distribution, the bounds are computed and compared.
Hamid Karamikabir, Mohammad Arashi,
Volume 8, Issue 1 (9-2014)
Abstract
In this paper we consider of location parameter estimation in the multivariate normal distribution with unknown covariance. Two restrictions on the mean vector parameter are imposed. First we assume that all elements of mean vector are nonnegative, at the second hand assumed only a subset of elements are nonnegative. We propose a class of shrinkage estimators which dominate the minimax estimator of mean vector under the quadratic loss function.
Anahita Nodehi, Mousa Golalizadeh,
Volume 8, Issue 1 (9-2014)
Abstract
Bivariate Von Mises distribution, which behaves relatively similar to bivariate normal distributions, has been proposed for representing the simultaneously probabilistic variability of these angles. One of the remarkable properties of this distribution is having the univariate Von Mises as the conditional density. However, the marginal density takes various structures depend on its involved parameters and, in general, has no closed form. This issue encounters the statistical inference with particular problems. In this paper, this distribution and its properties are studied, then the procedure to sample via the acceptance-rejection algorithm is described. The problems encountered in choosing a proper candidate distribution, arising from the cyclic feature of both angles, is investigated and the properties of its conditional density is utilized to overcome this obstacle.
Nasrin Moradi, Abdolreza Sayyareh, Hanieh Panahi,
Volume 8, Issue 1 (9-2014)
Abstract
In this article, the parameters of the Exponentiated Burr type III distribution have been estimated based on type II censored data using maximum likelihood method with EM algorithm and Bayesian approach under Gamma prior distributions against the squared error, linex and entropy loss functions. Importance sampling technique and Lindley's approximation method have been applied to evaluate these Bayes estimates. The results are checked by simulation study and analyzing real data of acute myelogeneous disease. The Bayes estimates are, generally, better than the MLEs and all estimates improve by increasing sample size.
Ehsan Kharati Koopaei, Soltan Mohammad Sadooghi Alvandi,
Volume 8, Issue 1 (9-2014)
Abstract
The coefficient of variation is often used for comparing the dispersions of populations that have different measurement systems. In this study, the problem of testing the equality of coefficients of variation of several Normal populations is considered and a new test procedure based on Wald test and parametric bootstrap approach is developed. Since all the proposed tests for this problem are approximate, it is important to investigate how well each test controls the type I error rate. Therefore, via a simulation study, first the type I error rate of our new test is compared with some recently proposed tests. Then, the power of our proposed test is compared with others.
Aref Khanjari Idenak, Mohammadreza Zadkarami, Alireza Daneshkhah,
Volume 8, Issue 2 (3-2015)
Abstract
In this paper a new compounding distribution with increasing, decreasing, bathtub shaped and unimodal hazard rate function is proposed. The new four-parameters distribution is a generalization of the complementary exponential power distribution. The raw-moments, density function of the order statistics, survival function, hazard rate function, quantiles, mean residual lifetime and reliability function are presented. The estimation of the new distribution in a special case Poisson complementary exponential power distribution is studied by the method of maximum likelihood and EM algorithm. Expression for asymptotic distribution for the maximum likelihood estimation of the parameters of the PCEP distribution are obtained and for determining the precision of the variance and covariance of the estimations, a simulation is used, Then experimental results are illustrated based on the real data set.
Ali Doostmoradi, Mohammadreza Zadkarami, Mohammadreza Akhoond, Aref Khanjari Idenak,
Volume 8, Issue 2 (3-2015)
Abstract
In this paper a new distribution function based on Weibull distribution is introduced. Then the characteristics of this new distribution are considered and a real data set is used to compare this distribution with some of the generalized Weibull distributions.
Ehsan Zamanzade,
Volume 8, Issue 2 (3-2015)
Abstract
In this paper, an improved mean estimator for unbalanced ranked set samples is proposed. The estimator is obtained by using the fact that distribution function of order statistics are stochastically ordered. Also, it is showed that this estimator is convergent and has better performance than its empirical counterpart in unbalanced ranked set samples.
Akbar Asgharzadeh, Mina Azizpour, Reza Valiollahi,
Volume 9, Issue 1 (9-2015)
Abstract
One of the drawbacks of the type II progressive censoring scheme is that the length of the experiment can be very large. Because of that, recently a new censoring scheme named as the type II progressively hybrid censored scheme has received considerable interest among the statisticians. In this paper, the statistical inference for the half-logistic distribution is discussed based on the progressively type II hybrid censored samples. The maximum likelihood estimator, the approximate maximum likelihood estimator and the Bayes estimator of parameter using Lindley approximation and MCMC method are obtained. Asymptotic confidence intervals, Bootstrap confidence intervals and Bayesian credible intervals are obtained. Different point and interval estimators are compared using Monte Carlo simulation. A real data set is presented for illustrative purposes.
Saba Aghadoust, Kamel Abdollahnezhad, Farhad Yaghmaei, Ali Akbar Jafari,
Volume 9, Issue 1 (9-2015)
Abstract
The log-normal distribution is used to describe the positive data that has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and alimentary science, etc. Comparison of means of several log-normal populations always has been in focus of researchers, but their test statistics are not easy to derive or extremely complicated for this comparisons. In this paper, the size and power of different testing methods including F-test, likelihood ratio test, generalized p-value approach and computational approach test are compared in a simulation study.
Shahram Yaghoubzadeh, Ali Shadrokh, Masoud Yarmohammadi,
Volume 9, Issue 1 (9-2015)
Abstract
In this paper, we introduce a new five-parameters distribution with increasing, decreasing, bathtub-shaped failure rate, called as the Beta Weibull-Geometric (BWG) distribution. Using the Sterling Polynomials, the probability density function and several properties of the new distribution such as its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, mean residual life, reversed mean residual life are obtained. The maximum likelihood estimation procedure is presented in this paper. Also, we compare the results of fitting this distribution to some of their sub-models, using to a real data set. It is also shown that the BWG distribution fits better to this data set.
Ali Aghamohammadi, Sakineh Mohammadi,
Volume 9, Issue 2 (2-2016)
Abstract
In many medical studies, in order to describe the course of illness and treatment effects, longitudinal studies are used. In longitudinal studies, responses are measured frequently over time, but sometimes these responses are discrete and with two-state. Recently Binary quantile regression methods to analyze this kind of data have been taken into consideration. In this paper, quantile regression model with Lasso and adaptive Lasso penalty for longitudinal data with dichotomous responses is provided. Since in both methods posteriori distributions of the parameters are not in explicit form, thus the full conditional posteriori distributions of parameters are calculated and the Gibbs sampling algorithm is used to deduction. To compare the performance of the proposed methods with the conventional methods, a simulation study was conducted and at the end, applications to a real data set are illustrated.
Sana Eftekhar, Ehsan Kharati-Koopaei, Soltan Mohammad Sadooghi-Alvandi,
Volume 9, Issue 2 (2-2016)
Abstract
Process capability indices are widely used in various industries as a statistical measure to assess how well a process meets a predetermined level of production tolerance. In this paper, we propose new confidence intervals for the ratio and difference of two Cpmk indices, based on the asymptotic and parametric bootstrap approaches. We compare the performance of our proposed methods with generalized confidence intervals in term of coverage probability and average length via a simulation study. Our simulation results show the merits of our proposed methods.
Abouzar Bazyari,
Volume 10, Issue 1 (8-2016)
Abstract
Hypothesis testing the homogeneity of means of k univariate normal populations against the hypothesis of one sided ordered means with unknown and equal variances is considered. A new completely method to find the uniformly most powerful test at significance level α is presented based on the multivariate t distribution. Since for more than two populations finding the null distribution of test statistic is not easy, the power of test is computed and then the critical values of test statistic for different significance levels obtained. This testing method is used for real examples. Also testing homogeneity of k mean vectors against two sided ordered mean vectors of multivariate normal populations is considered. Using Monte Carlo simulation the values of classical power of test for two bivariate and trivariate normal distributions at different significance levels are compared.
Azadeh Kiapour, Mehran Naghizadeh Qomi,
Volume 10, Issue 2 (2-2017)
Abstract
In this paper, an approximate tolerance interval is presented for the discrete size-biased Poisson-Lindley distribution. This approximate tolerance interval, is constructed based on large sample Wald confidence interval for the parameter of the size-biased Poisson-Lindley distribution. Then, coverage probabilities and expected widths of the proposed tolerance interval is considered. The results show that the coverage probabilities have a better performance for the small values of the parameter and are close to the nominal confidence level, and are conservative for the large values of the parameter. Finally, an applicable example is provided for illustrating approximate tolerance interval.
Nader Nematollahi,
Volume 10, Issue 2 (2-2017)
Abstract
In some applied problems we need to choose a population from the given populations and estimate the parameter of the selected population. Suppose k random samples are chosen from k populations with proportional hazard rate model or proportional reversed hazard rate model. According to a specified selection rule, it is desired to estimate the parameter of the best (worst) selected population. In this paper, under the entropy loss function we obtain the uniformly minimum risk unbiased (UMRU) estimator of the parameters of the selected population, and derived sufficient conditions for minimaxity of a given estimator. Then we find the class of admissible and inadmissible linear estimators of the parameters of the selected population and determine the class of dominators of a given estimator. We show that the UMRU estimator is inadmissible and compare the obtained estimators by plotting their risk functions.
Maliheh Heidari, Farzad Eskandari,
Volume 11, Issue 1 (9-2017)
Abstract
In this paper the issue of variable selection with new approach in finite mixture of semi-parametric regression models is studying, although it is supposed that data have Poisson distribution. When we use Poisson distribution, two problems such as overdispersion and excess zeros will happen that can affect on variable selection and parameter estimation. Actually parameter estimation in parametric component of the semi-parametric regression model is done by penalized likelihood approach. However, in nonparametric component after local approximation using Teylor series, the estimation of nonparametric coefficients along with estimated parametric coefficients will be calculated. Using new approach leads to a properly variable selection results. In addition to representing related theories, overdispersion and excess zeros are considered in data simulation section and using EM algorithm in parameter estimation leads to increase the accuracy of end results.
Azadeh Kiapour,
Volume 11, Issue 1 (9-2017)
Abstract
Usually, we estimate the unknown parameter by observing a random sample and using the usual methods of estimation such as maximum likelihood method. In some situations, we have information about the real parameter in the form of a guess. In these cases, one may shrink the maximum likelihood or other estimators towards a guess value and construct a shrinkage estimator. In this paper, we study the behavior of a Bayes shrinkage estimator for the scale parameter of exponential distribution based on censored samples under an asymmetric and scale invariant loss function. To do this, we propose a Bayes shrinkage estimator and compute the relative efficiency between this estimator and the best linear estimator within a subclass with respect to sample size, hyperparameters of the prior distribution and the vicinity of the guess and real parameter. Also, the obtained results are extended to Weibull and Rayleigh lifetime distributions.
Mehran Naghizadeh Qomi, Maryam Vahidian,
Volume 11, Issue 2 (3-2018)
Abstract
The problem of finding tolerance intervals receives very much attention in researches and is widely applied in industry. Tolerance interval is a random interval that covers a proportion of the considered population with a specified confidence level. In this paper, the statistical tolerance limits are expressed for lifetime of k out of n systems with exponentially distributed component lifetimes. Then, we compute the accuracy of proposed tolerance limits and the number of failures needed to attain a desired accuracy level based on type-II right censored data. Finally, we extend our results to the Weibull distribution.
Shahram Yaghoobzadeh,
Volume 11, Issue 2 (3-2018)
Abstract
In this paper, the maximum liklihood estimation, unbiased estimations with minimum variance, percentile estimation, best percentile estimation single-observation estimation and the best percentile estimation two-observations in class which are based on order statistics are calculated in two sections for probability density and cumulative distribution functions of the beta Weibull geometric distribution, specially with bathtub-shaped and unimodal failure rate which are useful for modeling of data related to reliability and lifetime. Furthermore, through the simulation method of Monte Carlo and calculation of average square of errors of estimators, they are subjected to comparisons ultimately, the desirable estimator in each section is determined.
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