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Likelihood ratio orderings of spacings of heterogeneous exponential random variables


  • Wen, Songqiao
  • Lu, Qingshu
  • Hu, Taizhong


Let X1,X2,...,Xn be independent exponential random variables such that Xi has failure rate [lambda] for i=1,...,p and Xj has failure rate [lambda]* for j=p+1,...,n, where p>=1 and q=n-p>=1. Denote by Di:n(p,q)=Xi:n-Xi-1:n the ith spacing of the order statistics , where X0:n[reverse not equivalent]0. It is shown that Di:n(p,q)[less-than-or-equals, slant]lrDi+1:n(p,q) for i=1,...,n-1, and that if [lambda][less-than-or-equals, slant][lambda]* then , and for i=1,...,n, where [less-than-or-equals, slant]lr denotes the likelihood ratio order. The main results are used to establish the dispersive orderings between spacings.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:4:p:743-756

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    References listed on IDEAS

    1. 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. 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.
    3. 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.
    4. Torrado Robles, Nuria & Lillo Rodríguez, Rosa Elvira, 2012. "Comparisons among spacings from two populations," DES - Working Papers. Statistics and Econometrics. WS 13958, Universidad Carlos III de Madrid. Departamento de Estadística.


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