Recurrence relations for quotient moments of the exponential distribution by record valeus

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let fXn; n ¸ 1g be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function(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 Exp(1). Then E Xr u(m) Xs+1 u(n) != 1 s E Xr u(m) Xs u(n¡1)!¡ 1 s E Xr u(m) Xs u(n) !and E Xr+1 u(m) Xs u(n) != 1 (r + 2) E Xr+2 u(m) Xs u(n¡1)!¡ 1 (r + 2) E Xr+2 u(m¡1) Xs u(n¡1) ! KCI Citation Count: 2