On some statistical models with a random number of observations

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Abstract

We extend some classical statistical inference to the case of a random number of observations with a stabilized distribution: namely, in the normal model, inference for the mean with known and unknown variance and inference for the variance. We describe some useful models for the number of observations obtained by truncation or translation of usual models given by integer-valued random variables: Poisson, binomial, geometric, and negative binomial. We present an efficient random search algorithm for the computation of the quantiles of the relevant statistics, we describe an interval estimation procedure for the extended model, and we propose a parametric bootstrap simulation study to validate the proposed procedure.

Original languageEnglish
Pages (from-to)805-823
Number of pages19
JournalJournal of Statistical Theory and Practice
Volume10
Issue number4
DOIs
Publication statusPublished - 1 Oct 2016

Keywords

  • hypothesis tests power function
  • interval estimation
  • random number of observations
  • Statistical inference

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