MOMENTS OF RANDOM VARIABLES BASED ON BERNOULLI TRIALS

In a set of n repeated Bernoulli trials where each trial results in an event E, the number of events materialized is a random variable. Even when the trials are not dependent, there do arise  situations where  it is tedious to find the probability distribution of this random variable. The paper expresses the moments of this random variable in terms of probabilities of particular events  providing  some of applications  of this result

ON QUASI MEDIANS OF A WEIBULL SAMPLE

A sample quasi median may be used to estimate the median of a distribution when information on the sample median is not available. This paper expresses moments of  Quasi medians of a Weibull sample  in terms of incomplete beta functions. A comparison of  quasi medians and  sample median is made for the purpose of estimating the median of  Weibull distribution when its shape  parameter assumes various values

Asymptotic expansion of the distribution of the Z statistic in discriminant analysis

This paper deals with the classification statistic Z due to John [4], which is a competitor to the Anderson statistic W in discriminant analysis with two multivariate normal populations. An asymptotic expansion of the distribution of Z as well as the associated probability of misclassification with respect to the three numbers of degrees of freedom is given. Some coefficients in the expansion for the latter are computed numerically and compared with those for W, which were given before by Okamoto.asymptotic expansion Z statistic discriminant analysis Anderson statistic W maximum likelihood procedure probability of misclassification minimax property