This paper obtains Lorenz ordering relationships among order statistics from log-logistic samples of possibly different sizes. Some results extend other families including the Lomax, Burr III and Burr XII distributions.

This note presents a nonparametric Bayesian approach to fitting a distribution to the survey data provided in Kilian and Zha (2002) regarding the prior for the half-life of deviations from purchasing power parity (PPP). A point mass at infinity is included. The unknown density is represented as...

This paper introduces a new, semi-parametric model for circular data, based on mixtures of shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial density model which is well known to provide good approximations to any density with finite support and it is...

A Bayesian hierarchical model for simultaneously estimating and partitioning probability density functions is presented. Individual density functions are flexibly modeled using Bernstein densities, which are mixtures of beta densities whose parameters depend only on the number of mixture...

The estimation of probability density functions is one of the fundamental aspects of any statistical inference. Many data analyses are based on an assumed family of parametric models, which are known to be unimodal (e.g., exponential family, etc.). Often a histogram suggests the unimodality of...

The objective of this article is to develop a computationally efficient estimator of the regression function subject to various shape constraints. In particular, nonparametric estimators of monotone and/or convex (concave) regression functions are obtained by using a nested sequence of Bernstein...

In the paper [A. Rababah, M. Alqudah, Jacobi-weighted orthogonal polynomials on triangular domains, J. Appl. Math. 3 (2005) 205–217.], Jacobi-weighted orthogonal polynomials Pn,r(α,β,γ)(u,v,w),α,β,γ−1 on the triangular domain T for values of α,β,γ−1 in the plane α+β+γ=0 are...