A note on the stability of the estimation of the exponential distribution

Laurence A. Baxter, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Bounds on the uniform distance between a χ22n distribution and the distribution of 2Σni = 1 Xi/μ, where X1, X2,..., Xn are n independent, identically distributed nonnegative random variables with common mean μ, are derived assuming that the Xi's are HNBUE or HNWUE or that a specific 'mechanism' is 'perturbing' an exponential distribution. These bounds are used to quantify the robustness of the sampling distribution of the usual test statistic for hypothesis tests on the mean of the exponential distribution to departures from exponentiality.

Original languageEnglish
Pages (from-to)37-41
Number of pages5
JournalStatistics and Probability Letters
Volume10
Issue number1
DOIs
StatePublished - Jun 1990

Keywords

  • Exponential distribution
  • HNBUE
  • HNWUE
  • chi-square distribution
  • probability metric
  • robustness
  • stability theory

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