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Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits

Author

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  • Adele H. Marshall

    (Queen’s University Belfast)

  • Mariangela Zenga

    (Università Milano-Bicocca)

Abstract

In the past few decades, Coxian phase-type distributions have become increasingly more popular as a means of representing survival times. In healthcare, they are considered suitable for modelling the length of stay of patients in hospital and more recently for modelling the patient waiting times in Accident and Emergency Departments. The Coxian phase-type distribution has not only been shown to provide a good representation of real survival data, but its interpretation seems reasonably initiative to the medical experts. The drawback, however, is fitting the distribution to the data. There have been many attempts at accurately estimating the Coxian phase-type parameters. This paper wishes to examine the most promising of the approaches reported in the literature to determine the most accurate. Three performance measures are introduced to assess the fitting process of the algorithms along with the likelihood values and AIC to examine the goodness of fit and complexity of the model. Previous research suggests that the fitting process is strongly influenced by the initial parameter estimates and the data itself being quite variable. To overcome this, one experiment in this research paper will use the same initial parameter values for each estimation and perform the fits on the data simulated from a Coxian phase-type distribution with known parameters.

Suggested Citation

  • Adele H. Marshall & Mariangela Zenga, 2012. "Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 71-86, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9174-y
    DOI: 10.1007/s11009-010-9174-y
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    References listed on IDEAS

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    1. Vincent Goulet & Christophe Dutang & Mathieu Pigeon, 2008. "actuar : An R Package for Actuarial Science," Post-Print hal-01616144, HAL.
    2. M. J. Faddy, 1994. "Examples of fitting structured phase–type distributions," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 10(4), pages 247-255.
    3. Dutang, Christophe & Goulet, Vincent & Pigeon, Mathieu, 2008. "actuar: An R Package for Actuarial Science," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i07).
    4. Mary A. Johnson, 1993. "Selecting Parameters of Phase Distributions: Combining Nonlinear Programming, Heuristics, and Erlang Distributions," INFORMS Journal on Computing, INFORMS, vol. 5(1), pages 69-83, February.
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    Cited by:

    1. Christian Acal & Juan E. Ruiz-Castro & David Maldonado & Juan B. Roldán, 2021. "One Cut-Point Phase-Type Distributions in Reliability. An Application to Resistive Random Access Memories," Mathematics, MDPI, vol. 9(21), pages 1-13, October.
    2. Boquan Cheng & Rogemar Mamon, 2023. "A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 142-187, January.

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