Journal of Statistical Research of Iran
Volume:15 Issue: 2, 2019

We have considered a perfect sample method for model selection of finite mixture models with either known (fixed) or unknown number of components which can be applied in the most general setting with assumptions on the relation between the rival models and the true distribution. It is, both, one or neither to be well-specified or mis-specified, they may be nested or non-nested. We consider mixture distribution as a complete-data (bivariate) distribution by prediction of missing data variable (unobserved variable) and show that this ideas is applicable to use Vuong's test for select optimum mixture model when number of components are known (fixed) or unknown. We have considered  AIC  and  BIC  based on the complete-data distribution. The performance of this method is evaluated by Monte-Carlo method and real data set, as Total Energy Production.

A longitudinal study refers to collection of a response variable and possibly some explanatory variables at multiple follow-up times. In many clinical studies with longitudinal measurements, the response variable, for each patient is collected as long as an event of interest, which considered as clinical end point, occurs. Joint modeling of continuous longitudinal measurements and survival time is an approach for accounting association between two outcomes which frequently discussed in the literature, but design aspects of these models have been rarely considered. This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion (BPC), where the determined sample sizes are given based on BPC. We determine the sample size based on treatment effect on both outcomes (longitudinal measurements and survival time). The sample size determination is performed based on multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed. All the implementations are performed using R2OpenBUGS package and R 3.5.1 software.

Imprecise measurement tools produce imprecise data. Interval,-valued (interval) data is one type of data which is usually used to deal with such imprecision. So, interval-valued variables have been used in the last decade. The relationships between the variables have recently been modeled by linear regression models. If interval response variables have any statistical distributions, the relationships are modeled in the linear models framework. In this paper, we propose new estimators for the parameters of an interval linear model under some conditions. Under the conditions, we demonstrate the theoretical adequacy of the estimators. Simulation studies and a real-life case study show the empirical adequacy and the practical applicability of the new estimators, respectively, under the conditions.

In this paper, we consider a new class of bivariate copulas and study their measures of association. Specifically, we propose a bivariate copula based distribution and obtain explicit expressions for the corresponding marginal and joint distributions of concomitants of generalized order statistics. Using these results, we provide the minimum variance linear unbiased estimator for the location and scale parameters of the concomitants of order statistics of Burr and logistic distributions. Then, we introduce a class of absolutely continuous bivariate distributions whose univariate margins are exponential distributions. In addition, we discuss their properties such as moment generating function, stress-strength probability and reliability of two component systems. Monte Carlo simulations are performed to highlight properties of the parameters estimates. Finally, we analyze two data sets to illustrate the flexibility and potential of the proposed distribution compared to several competing models.

In this paper, shrinkage and Bayesian shrinkage estimation of the expected length (l) in a M/M/1 queue system is considered. A shrinkage estimator of l is considered when a priori about l as l_0 is available. The bias and the risk of shrinkage estimators are derived under a scale-invariant squared error loss (SISEL) function. A class of Bayes shrinkage estimators for $l$ is proposed which is a generalization of Bayes shrinkage estimator and a relative performance of proposed estimators and the maximum likelihood estimator (MLE) is performed. A simulated data is given to illustrate the proposed results. Finally, we conclude with a summary of our contributions.

In this paper, we introduce and study quantile version of the Shannon entropy function via doubly truncated (interval) lifetime, which includes the residual and past lifetimes as special case. We aim to study the use of proposed measure in characterization of distribution functions. Further, we describe a stochastic order and a weighted distribution based on this entropy and show their properties. Finally, some results have been obtained for some distributions such as Uniform, Exponential, Pareto I, Power function and Govindarajulu. Also by analysing a real data the subject has been illustrated.