On Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings

Multivariate Dispersive Ordering of Generalized Order Statistics

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate condi- tions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivari- ate dispersive ordering of GOSs from one sample and Khaledi-Kochar mu...

Ordering Conditional Distributions of Spacings of Generalized Order Statistics

The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters, on which the generalized order statistics are based on, to establish the usual stochastic and the likelihood ratio orderings of general p-spacings by conditioning on the right tail of another lower indexed generalized order statistics. Some potential applications are also given.

Multivariate Dispersive Ordering of Generalized Order Statistics

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivariate dispersive ordering of GOSs from one sample and Khaledi-Kochar multivar...

Generalized Likelihood Ratio Statistics

Generalized Likelihood Ratio Statistics and Wilks Phenomenon

The likelihood ratio theory contributes tremendous success to parametric inferences. Yet, there is no general applicable approach for nonparametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting. Even if they exist, they are hard to find and can not be optimal as shown in this paper. We intr...

Stochastic Orderings among Order Statistics and Sample Spacings

In this paper we review some of the results obtained recently in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as non-identically distributed. But most of the time we shall be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters i...