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Classical and Bayesian estimation of $$P(X>Y)$$ P ( X > Y ) using upper record values from Kumaraswamy’s distribution

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  • Mustafa Nadar
  • Fatih Kızılaslan

Abstract

In this paper, maximum likelihood and Bayesian approaches have been used to obtain the estimation of $$P(X>Y)$$ P ( X > Y ) based on a set of upper record values from Kumaraswamy distribution. The existence and uniqueness of the maximum likelihood estimates of the Kumaraswamy distribution parameters are obtained. Confidence intervals, exact and approximate, as well as Bayesian credible intervals are constructed. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX) loss functions using the conjugate and non informative prior distributions. The approximation forms of Lindley (Trabajos de Estadistica 3:281–288, 1980 ) and Tierney and Kadane (J Am Stat Assoc 81:82–86, 1986 ) are used for the Bayesian cases. Monte Carlo simulations are performed to compare the different proposed methods. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Mustafa Nadar & Fatih Kızılaslan, 2014. "Classical and Bayesian estimation of $$P(X>Y)$$ P ( X > Y ) using upper record values from Kumaraswamy’s distribution," Statistical Papers, Springer, vol. 55(3), pages 751-783, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:751-783
    DOI: 10.1007/s00362-013-0526-x
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    References listed on IDEAS

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    1. Baklizi, Ayman, 2008. "Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3468-3473, March.
    2. Mustafa Nadar & Alexander Papadopoulos & Fatih Kızılaslan, 2013. "Statistical analysis for Kumaraswamy’s distribution based on record data," Statistical Papers, Springer, vol. 54(2), pages 355-369, May.
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    Cited by:

    1. Fatih Kızılaslan, 2018. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions," Statistical Papers, Springer, vol. 59(3), pages 1161-1192, September.
    2. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.
    3. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    4. Amulya Kumar Mahto & Yogesh Mani Tripathi, 2020. "Estimation of reliability in a multicomponent stress-strength model for inverted exponentiated Rayleigh distribution under progressive censoring," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1043-1069, December.
    5. A. Asgharzadeh & S. F. Bagheri & N. A. Ibrahim & M. R. Abubakar, 2020. "Optimal confidence regions for the two-parameter exponential distribution based on records," Computational Statistics, Springer, vol. 35(1), pages 309-326, March.
    6. Raj Kamal Maurya & Yogesh Mani Tripathi & Tanmay Kayal, 2022. "Reliability Estimation in a Multicomponent Stress-Strength Model Based on Inverse Weibull Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 364-401, May.

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