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On the Conjecture of Kochar and Korwar

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  • Torrado Robles, Nuria
  • Lillo Rodríguez, Rosa Elvira
  • Wiper, Michael Peter

Abstract

In this paper, we solve for some cases a conjecture by Kochar and Korwar (1996) in relation with the normalized spacings of the order statistics related to a sample of independent exponential random variables with different scale parameter. 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 give the proof of this conjecture for n=4 and for both spacing and normalized spacings. We also generalize some results to n>4

Suggested Citation

  • Torrado Robles, Nuria & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2009. "On the Conjecture of Kochar and Korwar," DES - Working Papers. Statistics and Econometrics. WS ws092108, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws092108
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    References listed on IDEAS

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    1. 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.
    2. 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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    Heterogeneous exponential distribution;

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