Abstract

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛<TEX>$X_n,n\qeq1$</TEX>｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F(<TEX>$chi$</TEX>) and probability density function(pdf) f(<TEX>$chi$</TEX>). Let <TEX>$Y_n\;=\;mas{X_1,X_2,...,X_n}$</TEX> for <TEX>$ngeq1$</TEX>. We say <TEX>$X_{j}$</TEX> is an upper record value of {<TEX>$X_{n},n\geq1$</TEX>}, if <TEX>$Y_{j}$</TEX>＞<TEX>$Y_{j-1}$</TEX>,j＞1. The indices at which the upper record values occur are given by the record times <TEX>${u( n)}n,\geq1$</TEX>, where u(n) = min{j｜j ＞u(n-l), <TEX>$X_{j}$</TEX>＞<TEX>$X_{u(n-1)}$</TEX>,n\qeq2$</TEX> and u(l) = 1. Suppose <TEX>$X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$</TEX> then E<TEX>$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$</TEX> E<TEX>$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$</TEX> - <TEX>$\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$</TEX> and E<TEX>$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$</TEX> = <TEX>$\frac{1}{(r+1)\beta}$</TEX> [E<TEX>$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$</TEX> - E<TEX>$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$</TEX> - (r+1)E<TEX>$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$</TEX>]