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Parameter estimation and computation of the Fisher information matrix for functions of phase type random variables

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  • Pavithra, Celeste R.
  • Deepak, T.G.

Abstract

Parameter estimation and statistical inference for the phase type (PH) class of distributions are significantly important while considering the role of PH random variables in stochastic models appearing across various disciplines. Estimation of the parameters and computation of the Fisher Information Matrix (FIM) for some functions of PH random variables g(X), which are random variables of the continuous type is the main objective here. The following two cases are considered: (i) the set g−1(y) has at most a finite number of elements for every real y and (ii) for every real number y,g−1(y) has either a countably infinite number of elements that form an arithmetic progression or no element. The parameter estimation and the FIM computation for some random variables which can be obtained as functions of the PH random variables are carried out numerically for illustrative purposes. Also, some standard distributions like Pareto and beta as well as some real life data are shown to be approximated by appropriate functions of phase type random variables.

Suggested Citation

  • Pavithra, Celeste R. & Deepak, T.G., 2022. "Parameter estimation and computation of the Fisher information matrix for functions of phase type random variables," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321001961
    DOI: 10.1016/j.csda.2021.107362
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    References listed on IDEAS

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    1. Julia S. Benoit & Wenyaw Chan & Rachelle S. Doody, 2015. "Joint coverage probability in a simulation study on continuous-time Markov chain parameter estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2531-2538, December.
    2. Ahn, Soohan & Kim, Joseph H.T. & Ramaswami, Vaidyanathan, 2012. "A new class of models for heavy tailed distributions in finance and insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 43-52.
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