On generating T-X family of distributions using quantile functions

On generating T-X family of distributions using quantile functions

The cumulative distribution function (CDF) of the T-X family is given by R{W(F(x))}, where R is the CDF of a random variable T, F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univariate distributions. Different choices of the R, F and W functions naturally lead to different families of dis...

On composition of generating functions

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...

Quantile Optimization for Heavy-tailed Distributions Using Asymmetric Signum Functions

In this paper, we present a provably convergent algorithm for computing the quantile of a random variable that does not require storing all of the sample realizations. We then present an algorithm for optimizing the quantile of a random function which may be characterized by a heavy-tailed distribution where the expectation is not defined. The algorithm is illustrated in the context of electric...

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...

vgam Family Functions for Quantile Regression