Maximum Likelihood Estimation for a Class of Multinomial Distributions Arising in Reliability.

摘要

Let X sub i, i=1,..., k be independent Bernoulli random variables with potentially different probabilities of success p sub i, i-1,..., k. This situation is denoted by X sub i approx B(1,pi), i=1,...,k. Let Y = sub over i = 1 to k of X sub i and assume that a random sample Y1, Y2, ..., Yn is available. The common distribution of these Y's is the k-fold convolution to be denoted *(i = 1 to k). This note concerns the estimation of the parameters of this convolution based on the Y sample via the method of maximum likelihood.