Showing papers by "Barry C. Arnold published in 1984"
TL;DR: In this article, a necessary and sufficient condition for the order statistics to form a Markov chain for (n ≥ 3) is that there does not exist any atom x 0 of the parent distribution F satisfying F(x 0-)>0 and F (x 0)<1.
26 citations
TL;DR: In this article, a series of independent Bernoulli trials is considered in which either an outcome of type A or type B occurs at each trial, and the series terminates when n outcomes of one type have occurred.
Abstract: A series of independent Bernoulli trials is considered in which either an outcome of type A or type B occurs at each trial. The series terminates when n outcomes of one type have occurred. Two observable random variables of interest are the total number of outcomes in the series and the number of outcomes of the “losing kind.” Two methods of approximation of the expectations of these random variables for large n are obtained and compared. The limiting distribution of the number of outcomes of the “losing kind” is considered when a beta distribution is assigned to p.
4 citations
TL;DR: It is shown that in dimensions ⩾ 2, the posterior mean yields an inconsistent estimator of the joint probability law, contrary to the common assumption that the prior law ‘washes out’ with large samples.
Abstract: In the competing risks/multiple decrement model, the joint distribution is often not identifiable given only the observed time of failure and the cause of failure. The traditional approach is consequently to assume a parametric model. In this paper we shall not do this, but rather assume a Bayesian stance, take a Dirichlet process as a prior distribution, and then calculate the posterior distribution given the data. In this paper we show that in dimensions ⩾ 2, the posterior mean yields an inconsistent estimator of the joint probability law, contrary to the common assumption that the prior law ‘washes out’ with large samples. For single decrement mortality tables however, the non-parametric Bayesian method allows a flexible method for adjusting a standard mortality table to reflect mortality experience, or covariate information.
3 citations