Alternative approach to moments of order statistics from one-parameter Weibull distribution

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

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ISSN: 1234-7655
eISSN: 2450-0291

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VOLUME 21 , ISSUE 1 (March 2020) > List of articles

Alternative approach to moments of order statistics from one-parameter Weibull distribution

Piyush Kant Rai / Anu Sirohi

Keywords : order statistics, survival function, moments, characteristic function

Citation Information : Statistics in Transition New Series. Volume 21, Issue 1, Pages 169-178, DOI: https://doi.org/10.21307/stattrans-2020-010

License : (CC BY-NC-ND 4.0)

Received Date : 31-December-2017 / Accepted: 28-November-2019 / Published Online: 18-March-2020

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ABSTRACT

The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in connection to survival function is used to obtain these moments and expected values. In addition the characteristic function of the above distribution is also obtained in the form of gamma functions. Further an illustration is shown to find the first two moments and expected value of the product of order statistics by using this approach.

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