2016/10/19 by Rose Baker, Baker, Rose, Tarak Kharrat +2
Decision Sciences · Mathematics · Social Sciences · #FOS: Computer and information sciences #Insurance, Mortality, Demography, Risk Management #Methodology (stat.ME) #Probability and Risk Models #Statistical Methods and Bayesian Inference #demographic modeling and climate adaptation #stat.ME #statistics methodology
paper · pdf · doi:10.48550/arxiv.1610.06157
20 pages, 6 figures
arxiv created 2016/10/19 · openalex publication_date 2016/10/19 · arxiv updated 2016/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. We calculate the count probabilities by repeatedly convolving the discretized distribution, and then correct them using Richardson extrapolation. When just one probability is required, a second algorithm is described, an adaptation of De Pril's method, in which the computation time does not depend on the ordinality, so that even high-order probabilities can be rapidly found. Any survival distribution can be used to model the inter-arrival times, which gives a rich class of models with great flexibility for modelling both underdispersed and overdispersed data. This work could pave the way for the routine use of these distributions as an additional tool for modelling event count data. An empirical example using fertility data illustrates the use of the method and was fully implemented using an R package Countr developed by the authors and available from the Comprehensive R Archive Network.