scholarly journals Stieltjes classes for discrete distributions of logarithmic type

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2533-2540
Author(s):  
Sofiya Ostrovska ◽  
Mehmet Turan
Keyword(s):  
Significant Role ◽  
Moment Problem ◽  
Probability Distributions ◽  
Infinite Family ◽  
Discrete Distributions ◽  
Discrete Case ◽  
Continuous Distributions ◽  
Absolutely Continuous ◽  
The Moment ◽  
Logarithmic Type

Stieltjes classes play a significant role in the moment problem since they permit to expose explicitly an infinite family of probability distributions all having equal moments of all orders. Mostly, the Stieltjes classes have been considered for absolutely continuous distributions. In this work, they have been considered for discrete distributions. New results on their existence in the discrete case are presented.

Solutions of the Al-Salam–Chihara and allied moment problems

2019 ◽  
Vol 18 (02) ◽  
pp. 185-210 ◽  
Author(s):  
Mourad E. H. Ismail
Keyword(s):  
Moment Problem ◽  
Sufficient Conditions ◽  
Infinite Family ◽  
Weight Functions ◽  
Moment Problems ◽  
Order Operator ◽  
Absolutely Continuous ◽  
Rodrigues Formula ◽  
Wilson Operator ◽  
The Moment

We study the moment problem associated with the Al-Salam–Chihara polynomials in some detail providing raising (creation) and lowering (annihilation) operators, Rodrigues formula, and a second-order operator equation involving the Askey–Wilson operator. A new infinite family of weight functions is also given. Sufficient conditions for functions to be weight functions for the [Formula: see text]-Hermite, [Formula: see text]-Laguerre and Stieltjes–Wigert polynomials are established and used to give new infinite families of absolutely continuous orthogonality measures for each of these polynomials.

Review of Probability Distributions

2018 ◽  
pp. 25-73
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Discrete Distributions ◽  
Continuous Distributions ◽  
R Language ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Analysis And Study ◽  
Waiting Lines

In Chapter 2, probability distributions are presented; the distributions exposed are those with more relation to the analysis and study of waiting lines; discrete distributions: binomial, geometric, Poisson; continuous distributions: uniform, exponential, erlang, and normal. Confidence intervals are calculated for some of the parameters of the distributions. A brief example of the generation of pseudorandom exponential times using a spreadsheet is presented. The chapter closes with the goodness-of-fit tests of probability distributions, especially the Anderson-Darling test. The statistical language of programming R is used in the exercises performed. Several codes are proposed in R Language to perform calculations automatically.

A Class of Tests for the Dispersive-Equivalence of two Probability Distributions

1992 ◽  
Vol 42 (1-2) ◽  
pp. 129-134 ◽  
Author(s):  
Leszek Marzec ◽  
Pawel Marzec
Keyword(s):  
Probability Distributions ◽  
Location Parameter ◽  
The Other ◽  
Subject Classification ◽  
Continuous Distributions ◽  
Absolutely Continuous ◽  
Distribution Free ◽  
Secondary 62G30 ◽  
Random Samples ◽  
Asymptotically Distribution Free

Based on independent random samples from two absolutely continuous distributions, asymptotically distribution-free and consistent tests are proposed for testing that two distributions are identical except for an unknown location parameter against the alternative that one is dispersive ordered with respect to the other. These tests are based on weighted combinations of ratios of spacings. AMS 1980 Subject Classification: Primary 62Gl0, secondary 62G30.

scholarly journals Hardy's condition in the moment problem for probability distributions

2012 ◽  
Vol 57 (4) ◽  
pp. 811-820 ◽  
Author(s):  
J Stoyanov ◽  
J Stoyanov ◽  
G D Lin ◽  
G D Lin
Keyword(s):  
Moment Problem ◽  
Probability Distributions ◽  
The Moment

The moment problem on perfect hypergroups

2016 ◽  
Vol 29 (2) ◽  
pp. 232-236
Author(s):  
A. S. Okb El Bab ◽  
Hossam A. Ghany
Keyword(s):  
Moment Problem ◽  
The Moment
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