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On the conjecture of Kochar and Korwar

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  • Torrado, Nuria
  • Lillo, Rosa E.
  • Wiper, Michael P.

Abstract

In this article, we partially solve a conjecture by Kochar and Korwar (1996) [9] in relation to the normalized spacings of the order statistics of a sample of independent exponential random variables with different scale parameters. In the case of a sample of size n=3, they proved the ordering of the normalized spacings and conjectured that result holds for all n. We prove this conjecture for n=4 for both spacings and normalized spacings and generalize some results to n>4.

Suggested Citation

  • Torrado, Nuria & Lillo, Rosa E. & Wiper, Michael P., 2010. "On the conjecture of Kochar and Korwar," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1274-1283, May.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1274-1283
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    References listed on IDEAS

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    1. Huaihou Chen & Taizhong Hu, 2008. "Multivariate likelihood ratio orderings between spacings of heterogeneous exponential random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 17-29, June.
    2. Wen, Songqiao & Lu, Qingshu & Hu, Taizhong, 2007. "Likelihood ratio orderings of spacings of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 743-756, April.
    3. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    4. Kochar, Subhash C & Korwar, Ramesh, 1996. "Stochastic Orders for Spacings of Heterogeneous Exponential Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 69-83, April.
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    Cited by:

    1. Torrado, Nuria & Lillo, Rosa E., 2013. "Likelihood ratio order of spacings from two heterogeneous samples," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 338-348.
    2. Zhang, Zhengcheng & Yang, Luyi & Yang, Yonghong, 2022. "The conditional spacings and their stochastic properties," Statistics & Probability Letters, Elsevier, vol. 186(C).

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