Sequential order statistics with an order statistics prior

• Published in: Journal of multivariate analysis 2010-09, Vol.101 (8), p.1826-1836
• Main Authors: Burkschat, M., Kamps, U., Kateri, M.
• Format: Article
• Language: English
• Subjects: Distribution theory; Erlang distribution; ETED; ETED Gamma distribution Erlang distribution Independent gamma priors Weinman multivariate exponential distribution; Exact sciences and technology; Gamma distribution; Independent gamma priors; Mathematics; Multivariate analysis; Nonparametric inference; Probability and statistics; Probability distribution; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Studies; Weinman multivariate exponential distribution
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2010.03.017

In the model of sequential order statistics, prior distributions are considered for the model parameters, which, for example, describe increasing load put on remaining components. Gamma priors are examined as well as priors out of a class of extended truncated Erlang distributions (ETED), which is introduced along with some properties. The choice of independent priors in both set-ups leads to respective independent, conjugate posterior distributions for the model parameters of sequential order statistics. Since, in practical applications, the model parameters will often be increasingly ordered, a multivariate prior is applied being the joint distribution of common ETED-order statistics. Whatever baseline distribution of the sequential order statistics is chosen, the joint posterior distribution turns out to be a Weinman multivariate exponential distribution. Posterior moments are given explicitly, and HPD credible sets for the model parameters are stated.