We present a new generalized family of skew two-piece skew-elliptical (GSTPSE) models and derive some its statistical properties. It is shown that the new family of distribution may be written as a mixture of generalized skew elliptical distributions. Also, a new representation theorem for a...

A modification of ranked set sampling (RSS) called moving extremes ranked set sampling (MERSS) is considered for the estimation of the scale parameter of scale distributions. A maximum likelihood estimator (MLE) is studied and its properties are obtained. We prove the MLE is an equivariant...

Dikta, Kvesic, and Schmidt proposed a model-based resampling scheme to approximate critical values of tests for model checking involving binary response data. Their approach is inapplicable when the binary response variable is not always observed, however. We propose a missingness adjusted...

The paper considers a volatility model which introduces a persistent, integrated or near-integrated, covariate to the standard GARCH(1, 1) model. For such a model, we derive the asymptotic theory of the quasi-maximum likelihood estimator. In particular, we establish consistency and obtain limit...

Bayes and frequentist estimators are obtained for the two-parameter Gompertz distribution (GD), as well as the reliability and hazard rate functions, using progressive first-failure censoring plan. We have examined Bayes estimates under symmetric and asymmetric loss functions. We show that the...

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the...

We present a new model of loss processes in insurance. The process is a couple (N,L) where N is a univariate Markov-modulated Poisson process (MMPP) and L is a multivariate loss process whose behavior is driven by N. We prove the strong consistency of the maximum likelihood estimator of the...

This paper proposes a method to implement maximum likelihood estimation of the dynamic panel data type 2 and 3 tobit models. The likelihood function involves a two-dimensional indefinite integral evaluated using "two-step" Gauss-Hermite quadrature. A Monte Carlo study shows that the quadrature...

The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the...