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The density of the parameter estimators when the observations are distributed exponentially

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Abstract

We present the probability density of parameter estimators whenN independent variables are observed, each of them distributed according to the exponential low (with some parameters to be estimated). The numberN is supposed to be small. Typically, such an experimental situation arises in problems of software reliability, another case is a small sample in the GLIM modeling. The considered estimator is defined by the maximum of the posterior probability density; it is equal to the maximum likelihood estimator when the prior is uniform. The exact density is obtained, and its approximation is discussed in accordance with some information-geometric considerations.

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Authors and Affiliations

  1. Department of Probability and Statistics, Faculty of Mathematics and Physics, Comenius University Bratislava, Mlynska dolina, 84215, Bratislava, Slovakia

    Andrej Pázman

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  1. Andrej Pázman
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Additional information

The main body of the paper has been prepared during the author’s visit in LMC/IMAG Grenoble, France, on the invitation of Université Joseph Fourier in January 1994.

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Pázman, A. The density of the parameter estimators when the observations are distributed exponentially. Metrika 44, 9–26 (1996). https://doi.org/10.1007/BF02614051

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  • DOI: https://doi.org/10.1007/BF02614051

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