Khoan T. Dinh

A characterization of matrix variate normal distribution

The joint normality of two random vectors is obtained based on normal conditional with linear regression and constant covariance matrix of each vector given the value of the other without assuming the existence of the joint density. This result is applied to a characterization of matrix variate normal distribution.

Exact EDF Goodness-of-Fit Tests for Inverse Gaussian Distributions

Abstract Exact EDF goodness-of-fit tests for inverse Gaussian (m, λ) distributions in different cases of unknown parameters are constructed. In the case m is unknown and λ is known, a chi-square test is also proposed. The powers of the tests are estimated by Monte Carlo method at several different alternative distributions.

Maximum Likelihood Estimators of Binomial Parameters under an Order Restriction

Abstract An elementary method for finding a restricted maximum likelihood estimator of a sequence of k + 1 binomial parameters p 1,p 2, …, pk , q is presented. The order restriction, Pi ≥ q (i = 1, …, k), arises in comparing k treatment groups with a control group. An algorithm to find these estimators is also given.

A REGRESSION CHARACTERIZATION OF INVERSE GAUSSIAN DISTRIBUTIONS AND APPLICATION TO EDF GOODNESS-OF-FIT TESTS

We give a new characterization of inverse Gaussian distributions using the regression of a suitable statistic based on a given random sample. A corollary of this result is a characterization of inverse Gaussian distribution based on a conditional joint density function of the sample. Application of this corollary as a transformation in the procedure to construct EDF (empirical distribution function) goodness-of-fit tests for inverse Gaussian distributions is also studied.

STABILITY OF A CHARACTERIZATION OF NORMAL DISTRIBUTIONS BASED ON THE FIRST TWO CONDITIONAL MOMENTS

A characterization of normal distributions of two independent random vari- ables X and Y with a finite E(X 2 ) basedon the linearity of E(X | X + Y) andthe ho- moscedasticity of var(X | X + Y) given by Rao (1976) is provedto be stable.