On a Skew Bimodal Normal–Normal distribution fitted to the Old-Faithful geyser data

The Bimodal Normal distribution introduced by Alavi (2011) is a symmetric distribution where its variance is three times the variance of the corresponding normal distribution. Azzalini (1985) introduced the univariate Skew Normal distribution to model asymmetry data. In this paper the Skew Bimodal Normal–Normal distribution is introduced as a skew-symmetric distribution generated by the cumulative function of standard normal. Some properties of the distribution and some methods for generating data from this distribution are introduced. The maximum likelihood estimation of parameters is obtained. The distribution is fitted to the Old Faithful Geyser data.     

A new alternative quantile regression model for the bounded response with educational measurements applications of OECD countries

This article introduces a new distribution with two tuning parameters specified on the unit interval. It follows from a ‘hyperbolic secant transformation’ of a random variable following the Weibull distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions over the unit interval is a motivation for the study. The main distributional structural properties of the new distribution are established. The different estimation methods and two simulation works have been derived for model parameters. Subsequently, we develop a related quantile regression model for further statistical perspectives. We consider two real data applications based on the educational measurements of both OECD and some non-members of OECD countries. Our regression model aims to relate the desire to get top grades on certain young students in the OECD countries with some of their Education and School Life Index such as reading performance, work environment at home, and paid work experience. It is shown that the elaborated quantile regression model has a better fitting power than famous regression models when the unit response variable possesses skewed distribution as well as two independent variables are significant in the statistical sense at any standard significance level for the median response.     

Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling

In this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation–maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.     

Post Gulf War Forum Learning after 11 September 2001

This article does not have an abstract     

Doubly reweighted estimators for the parameters of the multivariate t-distribution

The t-distribution (univariate and multivariate) has many useful applications in robust statistical analysis. The parameter estimation of the t-distribution is carried out using maximum likelihood (ML) estimation method, and the ML estimates are obtained via the Expectation-Maximization (EM) algorithm. In this article, we will use the maximum Lq-likelihood (MLq) estimation method introduced by Ferrari and Yang (2010 Ferrari, D., and Y. Yang. 2010. Maximum lq-likelihood estimation. The Annals of Statistics 38 (2):753–83.[Crossref], [Web of Science ®] , [Google Scholar]) to estimate all the parameters of the multivariate t-distribution. We modify the EM algorithm to obtain the MLq estimates. We provide a simulation study and a real data example to illustrate the performance of the MLq estimators over the ML estimators.