Randomly weighted averages with beta random proportions

A novel extension of randomly weighted averages

“…In this section, we first review some results of Homei (2012) and then modify them a little bit to fit in our framework for getting Theorem 1. We provide the conditional distribution of…”

Characterizations of arcsin and related distributions based on a new generalized unimodality

“…Remark 3.4 Though this Theorem (3.3) only applies under some very specific assumptions, it is a wild generalization of Conjecture 1.1. Also, some results of [13] and [8,10] are special cases of Theorem 3.3.…”

Exact Results for the Distribution of Randomly Weighted Sums

“…There have been many papers studying the distribution of randomly weighted sums. Papers published since 2020 have studied: inequalities for sums of randomly weighted random variables [1][2][3]; randomly weighted sums of conditionally dependent and dominated varying-tailed increments [4]; second-order tail behavior of randomly weighted heavytailed sums [5]; complete and complete moment convergence for randomly weighted sums [6]; approximations for the tail behavior of bidimensional randomly weighted sums [7,8]; complete convergence for randomly weighted sums of random variables satisfying some moment inequalities [9]; complete convergence and complete moment convergence for maximal randomly weighted sums [10]; asymptotic distributions of randomly weighted sums [11]; complete moment convergence for randomly weighted sums of extended negatively dependent sequences [12]; complete convergence for randomly weighted sums [13,14]; complete f -moment convergence for randomly weighted sums [15]; tail asymptotics of randomly weighted sums of dependent strong subexponential random variables [16]; sums of two dependent randomly weighted random variables [17]; tail behavior of randomly weighted sums of dependent subexponential random variables [18]; randomly weighted sums for multivariate Dirichlet distributions [19]; complete convergence and complete integral convergence for randomly weighted sums [20]; complete moment convergence for randomly weighted sums of negatively superadditive-dependent random variables [21]; complete moment convergence for the maximum of randomly weighted sums [22]; the Baum-Katz theorem for randomly weighted sums [23]; asymptotics for the joint tail probability of bidimensional randomly weighted sums [24]; complete moment convergence for randomly weighted sums [25]. Other highly cited papers studying the distribution of randomly weighted sums include [26][27][28][29][30].…”