#### Filter Results:

- Full text PDF available (21)

#### Publication Year

1998

2012

- This year (0)
- Last 5 years (1)
- Last 10 years (12)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Frank P. A. Coolen, Pauline Coolen-Schrijner, Ke-Jian Yan
- Rel. Eng. & Sys. Safety
- 2002

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)

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)

- Pauline Coolen-Schrijner, Frank P. A. Coolen
- Rel. Eng. & Sys. Safety
- 2007

Age replacement of technical units has received much attention in the reliability literature over the last four decades. Mostly, the failure time distribution for the units is assumed to be known, and minimal costs per unit of time is used as optimality criterion, where renewal reward theory simplifies the mathematics involved but requires the assumption… (More)

We consider a discrete-time Markov chain on the non-negative integers with drift to innnity and study the limiting behaviour of the state probabilities conditioned on not having left state 0 for the last time. Using a transformation, we obtain a dual Markov chain with an absorbing state such that absorption occurs with probability 1. We prove that the state… (More)

This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution – actually an infinite family of quasi-stationary distributions – if and only if absorption is… (More)

Nonparametric predictive inference (NPI) is a powerful frequentist statistical framework based only on an exchangeability assumption for future and past observations, made possible by the use of lower and upper probabilities. In this paper, NPI is presented for ordinal data, which are categorical data with an ordering of the categories. The method uses a… (More)

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)