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Estimation and testing procedures for the reliability functions of Kumaraswamy-G distributions and a characterization based on records. (English) Zbl 1425.62029

Summary: In this article, characterization based on record values for Kumaraswamy-G distributions is provided. Two measures of reliability are considered, namely \(R(t) = P(X>t)\) and \(P= P(X > Y)\). Point and interval estimation procedures are developed for unknown parameter(s), \(R(t)\) and \(P\), based on records. Two types of point estimators are considered, namely (1) uniformly minimum variance unbiased estimators and (2) maximum likelihood estimators. Testing procedures are also developed for the hypotheses related to various parametric functions. A comparative study of different methods of estimation is done through simulation studies. Real data example is used to illustrate the results.

MSC:

62E15 Exact distribution theory in statistics
62G30 Order statistics; empirical distribution functions
62G15 Nonparametric tolerance and confidence regions

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