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On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components

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  • Misra, Neeraj
  • Misra, Amit Kumar

Abstract

Let X1,…,Xn (Y1,…,Yn) be independent random variables such that Xi (Yi) follows the gamma distribution with shape parameter α and mean αλi(αμi), α>0,λi>0 (μi>0), i=1,…,n. Let λ=(λ1,…,λn), μ=(μ1,…,μn) and let r̃n:n(λ;x) (r̃n:n(μ;x)) denote the reversed hazard rate of max{X1,…,Xn} (max{Y1,…,Yn}). In this note we show that if λ weakly majorizes μ then r̃n:n(λ;x)≥r̃n:n(μ;x),∀x>0, thereby strengthening the results of Dykstra et al. (1997), and Lihong and Xinsheng (2005).

Suggested Citation

  • Misra, Neeraj & Misra, Amit Kumar, 2013. "On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1567-1570.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:6:p:1567-1570
    DOI: 10.1016/j.spl.2013.03.002
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    References listed on IDEAS

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    1. Lihong, Sun & Xinsheng, Zhang, 2005. "Stochastic comparisons of order statistics from gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 112-121, March.
    2. Proschan, F. & Sethuraman, J., 1976. "Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 608-616, December.
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    Cited by:

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    2. Mathew, Litty & P., Anisha & Kattumannil, Sudheesh K., 2022. "A jackknife empirical likelihood ratio test for strong mean inactivity time order," Statistics & Probability Letters, Elsevier, vol. 190(C).
    3. Zhao, Peng & Balakrishnan, N., 2014. "A stochastic inequality for the largest order statistics from heterogeneous gamma variables," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 145-150.
    4. Shovan Chowdhury & Amarjit Kundu, 2016. "Stochastic Comparison of Parallel Systems with Finite Range Distributed Components," Working papers 201, Indian Institute of Management Kozhikode.
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    6. Kundu, Amarjit & Chowdhury, Shovan, 2016. "Ordering properties of order statistics from heterogeneous exponentiated Weibull models," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 119-127.

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