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On Products and Mixed Sums of Gamma and Beta Random Variables Motivated by Availability

Author

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  • Hazhir Homei

    (University of Tabriz)

  • Saralees Nadarajah

    (University of Manchester)

Abstract

Motivated by the notion of availability, the exact distribution of the sum of beta random variables is derived under the impact of the environment. A suitable approximation is presented when the exact distribution cannot be identified. Also presented are some characterizations for the gamma distribution.

Suggested Citation

  • Hazhir Homei & Saralees Nadarajah, 2018. "On Products and Mixed Sums of Gamma and Beta Random Variables Motivated by Availability," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 799-810, June.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9591-2
    DOI: 10.1007/s11009-017-9591-2
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    References listed on IDEAS

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    1. S. Goli & M. Asadi, 2017. "A study on the conditional inactivity time of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 227-241, February.
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    3. Alamatsaz, M. H., 1993. "On characterizations of exponential and gamma distributions," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 315-319, July.
    4. Saralees Nadarajah & Samuel Kotz*, 2005. "On the Product and Ratio of Gamma and Beta Random Variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(4), pages 435-449, November.
    5. Rezapour, Mohsen & Alamatsaz, Mohammad Hossein, 2014. "Stochastic comparison of lifetimes of two (n−k+1)-out-of-n systems with heterogeneous dependent components," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 240-251.
    6. Saraless Nadarajah, 2006. "Exact and approximate distributions for the product of inverted Dirichlet components," Statistical Papers, Springer, vol. 47(4), pages 551-568, October.
    7. V. Nekoukhou & M. Alamatsaz, 2012. "A family of skew-symmetric-Laplace distributions," Statistical Papers, Springer, vol. 53(3), pages 685-696, August.
    8. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
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