On a Class of Recurrence Relations

Recurrence Relations for Moment Generating Functions of Generalized Order Statistics Based on Doubly Truncated Class of Distributions

In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

Quasi-regular Relations – a New Class of Relations on Sets

Following Jiang Guanghao and Xu Luoshan’s concept of conjugative, dually conjugative, normal and dually normal relations on sets, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasiregular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually ...

On the dynamics of certain recurrence relations

In recent analyses [3, 4] the remarkable AGM continued fraction of Ramanujan—denoted R1(a, b)—was proven to converge for almost all complex parameter pairs (a, b). It was conjectured that R1 diverges if and only if (0 = a = be with cos2 φ = 1) or (a2 = b2 ∈ (−∞, 0)). In the present treatment we resolve this conjecture to the positive, thus establishing the precise convergence domain for R1. Thi...

Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

A new class of function spaces on domains of R^d and its relations to classical function spaces