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.

This study offers a newly proposed distribution called alpha power Lomax (APL) distribution as a new extension of the Lomax distribution using the alpha power transformation (APT) method. Some distributional properties of newly defined distribution such as density function, moments, hazard and survival functions, orders statistics etc. are investigated. Parameters of the APL distribution are estimated with the help of the maximum likelihood (ML) estimation method. The applicability of the APL distribution is conducted through a simulation study and a real data example.

A bimodal extension of the generalized gamma distribution is proposed by using a mixing approach. Some distributional properties of the new distribution are investigated. The maximum likelihood (ML) estimators for the parameters of the new distribution are obtained. Real data examples are given to show the strength of the new distribution for modeling data.

The inverse Gaussian regression (IGR) model parameters are generally estimated using the maximum likelihood (ML) estimation method. Since the multicollinearity problem exists among the explanatory variables, the ML estimation method becomes inflated. When the multicollinearity problem occurs, biased estimators can be used to estimate the parameters of the model. One of the most widely used biased estimators is the Liu-type estimator. In this study, we extend the Liu-type estimator for the IGR model. The proposed estimator is compared with the Ridge and Liu estimators defined for the IGR model in terms of the mean squared error (MSE) criterion. Also, a real data example is presented to illustrate the superiority of the proposed estimator. Experimental results show that the Liu-type estimator outperforms the Ridge and Liu estimators when multicollinearity exists.