Following each abstract, identifies the name and address of the corresponding author. Canada Tail asymptotics of certain mixtures of Poisson distributions show that they are Paretian, their tail index being one of the parameters defining these laws. Estimators similar to those proposed by Press for continuous stable laws are then used for the estimation of the parameters of such laws and asymptotic properties are proved.
Inference is based on the empirical probability generating function.
As special cases the discrete stable distribution, the discrete Linnik distribution, and the Sibuya distribution are examined. The Pearson chi-squared is the most commonly used test statistic for testing the equality of two multinomial populations with nominal levels. For ordinal levels, typical test statistics are based on scorings of the ordinal levels, but the results of these tests are usually dependent on the choice of the increasing scores. In this paper we propose a test which does not depend on scores and has been constructed by making a natural modification in the chi-squared statistic to incorporate the ordinal information. Consider data arising from two independent samples of size m and n from two multinomial populations each having the same k categories.