Measures of Extropy for Concomitants of Generalized Order Statistics in Morgenstern Family

In this paper, a measure of extropy is obtained for concomitants of m-generalized order statistics in the Morgenstern family. The cumulative residual extropy (CREX) and negative cumulative extropy (NCEX) are presented for the rth concomitant of m-generalized order statistics. In addition, the problem of estimating the CREX and NCEX is studied utilizing the empirical method in concomitants of m-generalized order statistics. Some applications of these results are given for the concomitants of order statistics and record values.

The Extended Birnbaum–Saunders Distribution Based on the Scale Shape Mixture of Skew Normal Distributions

In this article, a large class of univriate Birnbaum–Saunders distributions based on the scale shape mixture of skew normal distributions is introduced which generates suitable subclasses for modeling asymmetric data in a variety of settings. The moments and maximum likelihood estimation procedures are disscused via an ECM-algorithm. The observed information matrix to approximate the asymptotic covariance matrix of the parameter estimates is then derived in some subclasses. A simulation study is also performed to evaluate the finite sample properties of ML estimators and finally, a real data set is analyzed for illustrative purposes.

A Test for Multiple Binary Endpoints with Continuous Latent Distribution in Clinical Trials

In clinical trials, two or more binary responses obtained by dichotomizing continuous responses are often employed as multiple primary endpoints. Testing procedures for multiple binary variables with latent distribution have not yet been adequately discussed. Based on the association measure among latent variables, we provide a statistic for testing the superiority of at least one binary endpoint. In addition, we propose a testing procedure with a framework in which the trial efficacy is confirmed only when there is superiority of at least one endpoint and non-inferiority of the remaining endpoints. The performance of the proposed procedure is evaluated through simulations.

Using Model Selection Criteria to Choose the Number of Principal Components

The use of information criteria, especially AIC (Akaike’s information criterion) and BIC (Bayesian information criterion), for choosing an adequate number of principal components is illustrated.

Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

Prediction based on a single linear regression model is one of the most common way in various field of studies. It enables us to understand the structure of data, but might not be suitable to express the data whose structure is complex. To express the structure of data more accurately, we make assumption that the data can be divided in clusters, and has a linear regression model in each cluster. In this case, we can assume that each explanatory variable has their own role; explaining the assignment to the clusters, explaining the regression to the target variable, or being both of them. Introducing probabilistic structure to the data generating process, we derive the optimal prediction under Bayes criterion and the algorithm which calculates it sub-optimally with variational inference method. One of the advantages of our algorithm is that it automatically weights the probabilities of being each number of clusters in the process of the algorithm, therefore it solves the concern about selection of the number of clusters. Some experiments are performed on both synthetic and real data to demonstrate the above advantages and to discover some behaviors and tendencies of the algorithm.