title: How old is this bird? The age distribution under some phase sampling schemes.
abstract: In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the individual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during the monitoring period 2007-2014.
authors.affiliation: School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia. sophiemh@unimelb.edu.au.|Institute of Mathematics, Ecole polytechnique fédérale de Lausanne, Lausanne, Vaud, Switzerland. sophiemh@unimelb.edu.au.
authors.forename: Sophie
authors.identifier: 0000-0002-8361-1901
authors.initials: S
authors.lastname: Hautphenne
authors.affiliation: Institute of Land, Water and Society, School of Environmental Sciences, Charles Sturt University, Albury, NSW, 2640, Australia.
authors.forename: Melanie
authors.initials: M
authors.lastname: Massaro
authors.affiliation: School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia.
authors.forename: Peter
authors.initials: P
authors.lastname: Taylor
mesh_terms: D017677:Age Distribution; D000818:Animals; D056808:Biostatistics; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D009520:New Zealand; D016012:Poisson Distribution; D020308:Songbirds / Q000254:growth & development; D013269:Stochastic Processes
keywords: Age distribution; Petroica traversi; Phase-type distribution; Transient Markov chain