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The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P (.) and ergodic matrix Π is the matrix D ≡ ∞ 0 (P (t) − Π)dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of… (More)

The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one… (More)

The purpose of this paper is to extend some results of Karlin and McGregor's and Chihara's concerning the three-terms recurrence relation for polynomials orthogonal with respect to a measure on the nonnegative real axis. Our findings are relevant for the analysis of a type of Markov chains known as birth-death processes with killing.

- F P A Coolen, P Coolen-Schrijner
- 2006

This paper presents several main aspects of Bayesian reliability demonstration, together with a concise discussion of key contributions to this topic.

1 SUMMARY In reliability and lifetime testing, comparison of two groups of data is a common problem. In some lifetime experiments, making a quick and efficient decision is desirable in order to save time and costs. To this end, a progressive censoring scheme can be useful, with censoring occurring at different stages [2]. This paper presents a nonparametric… (More)

- F P A Coolen, P Coolen-Schrijner
- 2005

We use the lower and upper predictive probabilities from Coolen [5] to compare future numbers of successes in Bernoulli trials for different groups. We consider both pairwise and multiple comparisons. These inferences are in terms of lower and upper probabilities that the number of successes in m future trials from one group exceeds the number of successes… (More)

Nonparametric predictive inference (NPI) is a statistical approach based on few assumptions about probability distributions, with inferences based on data. NPI assumes exchangeability of random quantities, both related to observed data and future observations, and uncertainty is quantified via lower and upper probabilities. In this paper, lifetimes of units… (More)

We consider opportunity-based age replacement using nonparametric predictive inference (NPI) for the time to failure of a future unit. Based on n observed failure times, NPI provides lower and upper bounds for the survival function for the time to failure X n+1 of a future unit, which lead to upper and lower cost functions, respectively, for… (More)