فهرست مطالب اکبر اصغرزاده

In this paper, the smallest confidence region is obtained for the location and scale parameters of the two-parameter exponential distribution. For this purpose, we use constrained optimization problems. We first provide some suitable pivotal quantities to obtain a balanced confidence region. We then obtain the smallest confidence region by minimizing the area of the confidence region using the Lagrangian method. Two numerical examples are presented to illustrate the proposed methods. Finally, some applications of proposed joint confidence regions in hypothesis testing and the construction of confidence bands are discussed.

This paper presents exact joint confidence regions for the parameters of the Rayleigh distribution based on record data. By providing some appropriate pivotal quantities, we construct several joint confidence regions for the Rayleigh parameters. These joint confidence regions are useful for constructing confidence regions for functions of the unknown parameters. Applications of the joint confidence regions using two environmental data sets are presented for illustrative purposes. Finally, a simulation study is conducted to study the performance of the proposed joint confidence regions.

This article presents the analysis of the Type-II hybrid progressively censored data when the lifetime distributions of the items follow Type-II generalized logistic distribution. Maximum likelihood estimators (MLEs) are investigated for estimating the location and scale parameters. It is observed that the MLEs can not be obtained in explicit forms. We provide the approximate maximum likelihood estimators (AMLEs) by appropriately approximating the likelihood equations. Asymptotic confidence intervals based on MLEs and AMLEs and one bootstrap confidence interval are proposed.
Estimation of the shape parameter is also discussed. Monte Carlo simulations are performed to compare the performances of the different methods and two real data sets have been analyzed for illustrative purposes.

This paper deals with the problem of reconstructing missing data in a left type-II censoring scheme, where the underlying distribution is the Weibull distribution. Frequentist and Bayesian approaches are adopted in order to provide some point reconstructors for the past failure times. The problem of determining reconstruction intervals for the past failure times is also considered. The investigation includes an example of application to real data and various comparisons based on Monte Carlo simulations.

Nadarajah and Haghighi (2011) introduced a new generalization of the exponential distribution as an alternative to the gamma, Weibull and exponeniated exponential distributions. In this paper, a generalization of the Nadarajah– Haghighi (NH) distribution namely exponentiated generalized NH distribution is introduced and discussed. The properties and applications of proposed model to real data are discussed. A Monte Carlo simulation experiment will be conducted to evaluate the maximum likelihood estimators of unknown parameters.

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.

In this paper, we consider the estimation of the unknown parameter of the scaled logistic distribution on the basis of record values. The maximum likelihood method does not provide an explicit estimator for the scale parameter. In this article, we present a simple method of deriving an explicit estimator by approximating the likelihood function. Bayes estimator is obtained using importance sampling. Asymptotic confidence intervals,bootstrap confidence interval and credible interval are also proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of one real data set is also given for illustrative purposes.

For computing different point estimates such as method of moment and maximum like-lihood estimates and different interval estimates (classical confidence interval، unbi-ased confidence interval، HPD interval)، we may deal with the equations which need be solved numerically. In this paper، some numerical methods for solving these type of equations are reviewed in S-PLUS package. Various examples are presented to illus-trate the methods described.

In this paper، we discuss different predictors of times to failure of units censored in a hybrid censored sample from exponential distribution. Bayesian and non-Bayesian point predictors for the times to failure of units are obtained. Non-Bayesian prediction intervals are obtained based on pivotal and highest conditional density methods. Bayesian prediction intervals are also proposed. One real data set has been analyzed to illustrate all the prediction methods. Finally، different prediction methods have been compared using Monte Carlo simulations.

In this paper, we study the estimation problems for the Burr type III distribution based on a complete sample. The maximum likelihood method is used to derive the point estimators of the parameter. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Two numerical examples with real data set and simulated data, are presented to illustrate the methods proposed here.

In this paper، we introduce the half-logistic distribution. The moments، skewness and kurtosis coe±cients re obtained. The maximum likelihood method does not provide an explicit estimator for the scale parameter. We provides a simple method of deriving an explicit estimator by approximating the likelihood function and study the e±ciency of this method by simulation.

In this paper, the balanced loss function (BLF) which reflects both the goodness of fit and the precision of estimation are considered. The estimation of a normal mean and the admissibility of all linear estimations of the sample mean X are studied.