Determination of Optimal Block Designs With Pre-assigned Variance For Elementary Contrasts

A method for obtaining optimal designs from the class of variance balanced and connected designs was developed for comparing treatment effects with a pre-assigned variance. The properties of the C-matrix of a block design are employed in developing this method. Some new results concerning the design parameters and the non-zero characteristic root of the C-matrix are also presented

On some Integral Representations of Certain G-Functions

This is a brief exposition of some statistical techniques utilized to obtain several useful integral equations involving G-functions

Distribution of the LR criterion Up,m,n as a marginal distribution of a generalized Dirichlet model

The density of the likelihood ratio criterion Up,m,n is expressed in terms of a marginal density of a generalized Dirichlet model having a specific set of parameters. The exact distribution of the likelihood ratio criterion so obtained has a very simple and general format for every p . It provides an easy and direct method of computation of the exact p -value of Up,m,n . Various types of properties and relations involving hypergeometric series are also established

Distribution of the LR criterion Up,m,n as a marginal distribution of a generalized Dirichlet model

The density of the likelihood ratio criterion Up,m,n is expressed in terms of a marginal density of a generalized Dirichlet model having a specific set of parameters. The exact distribution of the likelihood ratio criterion so obtained has a very simple and general format for every p . It provides an easy and direct method of computation of the exact p -value of Up,m,n . Various types of properties and relations involving hypergeometric series are also established

A generalized Dirichlet model

A generalized Dirichlet model is introduced which extends the standard real type-2 Dirichlet density. Many properties of this new model are studied. Various types of properties are also derived which enhance the possibility of applications in different directions.Generalized Dirichlet distribution Product moments Transformations of variables Type-1 and type-2 beta Dirichlet models