Calcutta Statistical Association Bulletin

General relations between directional majorization and multi variate majorization are studied, and sufficient conditions for directional majorization not to imply multivariat majorization are obtained.

A pth order integer valued autoregressive process having minification structure is introduced and its solution, in the stationary case, is obtatned. This result gives rise to a characterization of the well known discrete Pareto type III (Zipf_III) distribution.

Interesting characterizations of the exponential distribution have been obtained in classes of life distributions important in reliability theory. The results strengthen some of the analogous conclusions already existing in the literature.

AMS (1991) Subject Classification No. Primary 62NOS: Secondaey 90825. 60F99.

When the hypothesis of equality of means of several univariate homoscedastic normal populations from which independent samples are available, is rejected on the basis of the ANOV A F-test, the populations have to be divided into disjoint groups such that within each group the populations are all same. For any such division a natural index of correctness of the grouping is defined and a procedure is proposed such that it leads to the choice of a division for which the true index does not fall below a stipulated threshold at a given level of confidence. The procedure is illustrated through some numerical examples.

Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.

A class of estimators for a finite population mean is presented for the situations where population means of some auxiliary variables are known while those of others are unknown. The results for general two phase sampling are indicated while the detailed discussion is made for the case when SRSWOR is used at both the phases. While several known estimators belong to the proposed clas~ some new estimators are identified as well. The optimum estimator in the proposed class is found to be better than the so-called chain ratio and regression estimators discu ssed by Chand (1975). Kiregyera (1984) and Mukerjee et al. (1987). The relative gains in efficiency of tho proposed optimum estimator over the others are obtained for a natural population data and found to be quite appreciable.

The problem considered is that of finding designs in case of inadequacy in the model of a mixture experiment. Box and Draper (1959) proposed for comparing designs, the Integrated Mean Square Error (IMSE) criterion which is composed of integrated variance and integrated bias. A class of augmented axial designs Δ q = { Δ   ( δ 1 ,     δ 2   ;     a ,     β ,     q )   ;     0 ⩽ δ 1 ⩽ q − 1 q ,     0 ⩽ δ 2 ⩽ 1 q ;     0 ⩽ a ,     β ;     a + β ⩽ 1 } is proposed and is used to find the all-variance and all-bias designs for the first and second degree model.

Nearly balanced uniform repeated measurement designs are defined and construction of such designs when the number of units is less than or equal to the number of treatments and the numbers of periods is less than the number of treatments, is given.

AMS (1980) subject classification : 62K05.

Berry-Bsseen bounds with random norming and Jario deviation probabilities arc derived for the maximum likelihood estimator of the drift parameter in tho Ornstoin-Uhlenbeck proccss.

AMS (1991) Subject Classification: Primary 62F12, 62M05 Secondary 60FOS, 60F10

New cyclic solutions of several group divisible incomplete block designs arc presented, A new group divisible desian is reported whose solution is also cyclic. We also present non-isomorphic solutions of several group divisible designs listed in the catalogue of Clatworthy (1973).