Journal of the Iranian Statistical Society
Year:2018 | Volume:17 | Issue:1|Papers Count:6

The aim of statistical modeling is to identify the model that most closely ap-proximates 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 prin-ciple are derived. Also, asymptotic distribution of the normalized difference of AICs is obtained and it is used to construct an interval, say tracking interval, for compar-ing the two competing models. Monte Carlo simulations are performed to examine how the proposed interval works for different censoring schemes. 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.

In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfo-lio. 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 consid-ering 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.

In the restricted elliptical linear model, an approximation for the risk of a general shrinkage estimator of the regression vector-parameter is given. Superiority condition of the shrinkage estimator over the restricted estimator is investigated under the elliptical assumption. It is evident from numerical results that the shrinkage esti-mator performs better than the unrestricted one in the multivariate t-regression model.

In this paper, we introduce a new class of bivariate distributions by com-pounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate general-ized exponential-logarithmic, bivariate generalized exponential-binomial and bivari-ate generalized exponential-negative binomial distributions as special cases. We derive different properties of the proposed class of distributions. It is observed that the pro-posed class of bivariate distributions is a very flexible class of distribution functions. The joint probability density functions can have a variety of shapes. It can be bimodal as well as heavy tailed 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 ob-served that the proposed model and the EM algorithm work quite well in practice.

In this paper, borrowing the intuition in Rao et al. (2004), we introduce a cumulative version of the inaccuracy measure (CIM). Also we obtain interesting and applicable properties of CIM for different cases based on the residual, past and inter-val lifetime random variables. Relying on various applications of stochastic classes in reliability and information theory fields, we study new classes of the lifetime in terms of the CIM along with their relations with other famous aging classes. Furthermore, some characterization results are obtained under the proportional reversed hazard rate model. Finally, considering that the time t changes in the range (t1; t2), an extension of the CIM, called the interval cumulative residual (past) inaccuracy (ICR(P)I), is de-rived. We investigate the ICRI’ s relation with its analogous version based on Shannon entropy.

Recently, it has been observed that a new method for generating continuous distributions, T 􀀀 X family, can be quite effectively used to analyze the data in one dimension. The aim of this study is to generalize this method to two dimensional space so that the marginals would have T 􀀀 X distributions. 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, is fitted to a data set and is shown to have a better fit.