The likelihood ratio test foe the homogeneity of the variances in a covariance matrix with block compound symmetry

For the problem of testing the homogeneity of the variances in a covariance matrix with a block compound symmetric structure, the likelihood ratio test is derived in this paper, A modification of the test that allows its distribution to be better approximated by the chi-square distribution is also considered, Formulae for calculating approximate sample size and power are derived, Small sample performances of these tests in the case of two dependent bivariate or trivariate normals are compared to each other and to the competing tests by simulating levels of significance and powers, and recommendation is made of the ones that have good performance, The recommended tests are then demonstrated in an illustrative example.     

Maximum likelihood estimation,from doubly censored samples,of the mean of a normal distribution with known coeffucient of variation

Let x be a random variable having the normal distribution with mean μ and variance c²μ², where c is a known constant. The maximum likelihood estimation of μ when the lowest r₁ and the highest r₂ sample values censored have been given the asymptotic variance of the maximum likelihood estimator is obtained.     

A note on the estimation of the mixing parameter in a mixture of two distributions

Various classical methods of estimation are compared with those proposed by From (1989) for the estimation of the mixing parameter in a mixture of two distributions. Emphasis is put on the actual implementation of the estimation methods.