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- P Coolen-Schrijner, E A Van Doorn, Pauline Coolen-Schrijner, Erik A Van Doorn
- 2001

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)

- Pauline Coolen-Schrijner, Erik A Van Doorn
- 2004

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.

- Pauline Coolen-Schrijner, Erik A Van Doorn
- 2006

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)

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)

Nonparametric predictive inference (NPI) is a powerful fre-quentist 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)

- P Coolen-Schrijner, E A Van Doorn, Pauline Coolen-Schrijner, Erik A Van Doorn
- 2000

Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∞ 0 [lim u→∞ E(X(u)) − E(X(t))]dt as a measure of the speed of convergence towards stationarity of the process {X(t), t ≥ 0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t),… (More)

- P Coolen-Schrijner, E A Van Doorn, Pauline Coolen-Schrijner, Erik A Van Doorn
- 2005

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.

- P Coolen-Schrijner, E A Van Doorn, Pauline Coolen-Schrijner, Erik A Van Doorn
- 2004

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)