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Estimation and Testing Procedures for the Reliability Functions of Kumaraswamy-G Distributions and a Characterization Based on Records

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Abstract

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.

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Acknowledgements

The authors are thankful to the editor and referees for their valuable suggestions and comments which led to considerable improvement in the original version.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences, New Academic Block, University of Delhi, Delhi, 110007, India

    Taruna Kumari & Ajit Chaturvedi

  2. Department of Statistics, Ramjas College, University of Delhi, Delhi, 110007, India

    Anupam Pathak

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  1. Taruna Kumari
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  2. Ajit Chaturvedi
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  3. Anupam Pathak
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Correspondence to Anupam Pathak.

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Kumari, T., Chaturvedi, A. & Pathak, A. Estimation and Testing Procedures for the Reliability Functions of Kumaraswamy-G Distributions and a Characterization Based on Records. J Stat Theory Pract 13, 22 (2019). https://doi.org/10.1007/s42519-018-0014-7

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