Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A two-parameter discrete distribution with a bathtub hazard shape

  • Sarhan, Ammar M. (Department of Mathematics and Statistics, Dalhousie University)
  • Received : 2016.05.26
  • Accepted : 2016.12.19
  • Published : 2017.01.31
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Abstract

This paper introduces a two-parameter discrete distribution based on a continuous two-parameter bathtub distribution. It is the only two-parameter discrete distribution that shows a bathtub-shaped hazard function. Some statistical properties of the distribution are discussed. Three different methods are used to estimate its two unknown parameters. The point estimators of the parameters have no closed form. The bootstrap method is used to estimate the distributions of these point estimators. Different approximations of the interval estimations for the two-parameters are discussed. Real data sets are analyzed to show how this distribution works in practice. A simulation study is performed to investigate the properties of the estimations obtained and compare their performances.

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References

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