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The distribution of the sum of independent and non identically generalized Lindley random variables

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  • Masato Kitani
  • Hidetoshi Murakami
  • Hiroki Hashiguchi

Abstract

The original or generalized Lindley distribution has been proposed in order to fit a stochastic model to real data, that is, it establishes the distribution of the sum of independent variables. The distribution of the sum of independent and non identically generalized Lindley random variables is obtained by using inverse transformation of the moment generating function. A saddlepoint and a normal approximations are used to approximate the derived distribution. The accuracy of the approximations is shown by numerical simulations.

Suggested Citation

  • Masato Kitani & Hidetoshi Murakami & Hiroki Hashiguchi, 2023. "The distribution of the sum of independent and non identically generalized Lindley random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(8), pages 2597-2609, April.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:8:p:2597-2609
    DOI: 10.1080/03610926.2021.1955387
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