Recurrence Relations for Quotient Moments of the Pareto Distribution by Record Values
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Abstract
In this paper we establish some recurrence relations satis¯ed by quo- tient moments of upper record values from the Pareto distribution. Let fXn; n ¸ 1g be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F(x) and probability density func- tion(pdf) f(x). Let Yn = maxfX1;X2; : : : ;Xng for n ¸ 1. We say Xj is an upper record value of fXn; n ¸ 1g, if Yj > Yj¡1; j > 1. The indices at which the upper record values occur are given by the record times fu(n)g; n ¸ 1, where u(n) = minfjjj > u(n ¡ 1);Xj > Xu(n¡1); n ¸ 2g and u(1) = 1. Suppose X 2 PARµ1 ¯ ; 1 ¯¶ then E ÃXr u(m) Xs+1 u(n) != 1 s E à Xr u(m) Xs u(n¡1)!¡ (1 + ¯s) s E ÃXr u(m) Xs u(n) ! and E ÃXr+1 u(m) Xs u(n) != 1 (r + 1)¯ "E à Xr+1 u(m) Xs u(n¡1)!¡ E ÃXr+1 u(m¡1) Xs u(n¡1) !¡ (r + 1)E ÃXr u(m) Xs u(n) !#
참고문헌 (8)
- M. Ahsanuallah, "Record Statistics" (1995), Nova Science Publishers Inc
- Arnold, "rst course in order statistics Wiley Series in Probability and Mathematical Statistics" (1992), Inc
- no, "Recurrence relations for single and product mo-ments of record values from generalized Pareto distribution", pp.~23 (1994)
- "Relations for single and product moments of record values from exponentialdistribution", 2(1), pp.73~87 (1995)
- Chan, "Relations for single and product mo-ments of record values from Gumbel distribution" (1992)
- no, "Recurrence relations for moments of record values from generalized extremevalue distribution" (1993)
- Kotz, "Characterizations of probability distributions ed ap-proach with an emphasis on exponential and related models Lecture Notes in Mathe-matics" (1978)
- M. Y. Lee, "Characterizations of the Pareto distribution by conditional expectations ofrecord values", 18(1), pp.127~131 (2003), Dankook University Dankook University