Metrika

, 44:9 | Cite as

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

  • Andrej Pázman
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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.

Key Words

Exponential law maximum likelihood posterior modus densities of estimators I-divergence geometry in statistics reliability GLIM 
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Copyright information

© Physica-Verlag 1996

Authors and Affiliations

  • Andrej Pázman
    • 1
  1. 1.Department of Probability and Statistics, Faculty of Mathematics and PhysicsComenius University Bratislava, Mlynska dolinaBratislavaSlovakia

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