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Relations for marginal and joint moment generating functions of record values from power function distribution. (English) Zbl 0973.60055

Consider the record values \(\{R_n, n\geq 1\}\) arising from a sequence of i.i.d. random variables from a power function distribution (Pearson’s type I distribution) with pdf \(f(x;\gamma)= \gamma(1- x)^{\gamma-1}\), \(0< x< 1\), \(\gamma>0\). For \(\gamma= 1\), the distribution becomes the standard uniform distribution. The authors establish some recurrence relations for the marginal and joint moment generating functions of record values \(\{R_n\}\). The case of the moment generating functions of \(k\)-record values is also considered.

MSC:

60G70 Extreme value theory; extremal stochastic processes
60E05 Probability distributions: general theory
62E15 Exact distribution theory in statistics
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