Estimation of the ratio of a geometric process

Volume 44 / 2017

Alicja Jokiel-Rokita, Rafał Topolnicki Applicationes Mathematicae 44 (2017), 105-121 MSC: Primary 62F10; Secondary 62G05. DOI: 10.4064/am2316-12-2016 Published online: 3 March 2017

Abstract

We propose some estimators of the ratio parameter of a geometric process, i.e. of a stochastic process $\{X_{i},i=1,2,\ldots \}$ for which there exists a positive real number $a,$ called the ratio parameter, such that $\{Y_{i}=a^{i-1}X_{i},\,i=1,2,\ldots \}$ forms a renewal process. We assume that the cumulative distribution function $F$ of the random variables $Y_{i},$ $i=1,2, \ldots ,$ is completely unknown. We compare the accuracy of the proposed estimators of the ratio with known estimators given by Lam (1992) and by Chan et al. (2006), and also with the maximum likelihood estimators derived under the assumption that $F$ has a known form.

Authors

  • Alicja Jokiel-RokitaFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Rafał TopolnickiFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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