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Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution

Author

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  • Yadav Abhimanyu Singh

    (Department of Statistics, Banaras Hindu University, Varanasi, - 221005, India .)

  • Singh S. K.

    (Department of Statistics, Banaras Hindu University, Varanasi, - 221005, India .)

  • Singh Umesh

    (Department of Statistics, Banaras Hindu University, Varanasi, - 221005, India .)

Abstract

The aim of this paper is to introduce a new weighted probability distribution to model the non-monotone failure rate pattern for survival data. The proposed distribution is generalized by considering inverted Rayleigh distribution as a baseline distribution called an extended weighted inverted Rayleigh distribution. Different statistical properties such as moment, quantile function, moment generating function, entropy measurement, Bonferroni and Lorenz curve, stochastic ordering and order statistics have been derived. Different estimation procedures have also been discussed to estimate the unknown parameters of the proposed probability distribution. The Monte Carlo simulation study has been conducted to compare the performances of the proposed estimators obtained through various methods of estimation. Finally, two real data sets have been used to show the applicability of the proposed model in a real-life scenario.

Suggested Citation

  • Yadav Abhimanyu Singh & Singh S. K. & Singh Umesh, 2020. "Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 119-141, June.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:2:p:119-141:n:11
    DOI: 10.21307/stattrans-2020-016
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    References listed on IDEAS

    as
    1. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
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