论文信息 - Stochastic comparisons of spacings from restricted families of distributions

Stochastic comparisons of spacings from restricted families of distributions

Abstract Let X1:n⩽X2:n⩽⋯⩽Xn:n denote the order statistics of a random sample X1,…,Xn from a distribution F with support (0,∞). Let the generalized spacings [resp. spacings, normalized spacings and dual normalized spacings] of the X-sample be defined by U j,i:n =X j:n −X i:n , 0⩽i , [resp. U i:n =X i:n −X i−1:n , C i:n =(n−i+1)U i:n and C i:n =(i−1)U i:n ] with X0:n=0. We establish some comparison results for the generalized spacings in one-sample and two-sample problems, and also give some results for spacings complementing some known results in the literature.

Taizhong Hu | Taizhong Hu | Ying Wei | Ying Wei | Taizhong Hu

[1] Subhash C. Kochar,et al. On tail-ordering and comparison of failure rates , 1986 .

[2] Moshe Shaked,et al. Stochastic orders and their applications , 1994 .

[3] Subhash C. Kochar,et al. Some results on normalized spacings from restricted families of distributions , 1995 .

[4] Richard E. Barlow,et al. INEQUALITIES FOR LINEAR COMBINATIONS OF ORDER STATISTICS FROM RESTRICTED FAMILIES , 1966 .

[5] C. R. Rao,et al. Handbook of Statistics 17: Order Statistics-Applications , 2000, Technometrics.

[6] Harshinder Singh,et al. Preservation of partial orderings under the formation of k-out-of-n:G systems of i.i.d. components , 1991 .

[7] Harshinder Singh,et al. The Reversed Hazard Rate Function , 1998, Probability in the Engineering and Informational Sciences.

[8] Subhash C. Kochar,et al. Stochastic orderings between distributions and their sample spacings – II , 1999 .

[9] M. Shaked,et al. The Hazard Rate and the Reversed Hazard Rate Orders, with Applications to Order Statistics , 2001 .

[10] D. Yao,et al. Bivariate characterization of some stochastic order relations , 1991, Advances in Applied Probability.

[11] C. R. Rao,et al. Handbook of Statistics 16: Order Statistics-Theory and Methods , 2000, Technometrics.

[12] Syed N. U. A. Kirmani,et al. On sample spacings from IMRL distributions , 1998 .

[13] Moshe Shaked,et al. Preservation of some likelihood ratio stochastic orders by order statistics , 2001 .