A Moment Preserving Finitization Across the Power Series Family of Probability Distributions

2012 ◽  
Vol 41 (4) ◽  
pp. 653-664 ◽  
Author(s):  
Martin S. Levy ◽  
James J. Cochran ◽  
Saeed Golnabi
Keyword(s):  
Power Series ◽  
Probability Distributions

Burmann-series distributions and approximation operators

2005 ◽  
Vol 42 (4) ◽  
pp. 355-369
Author(s):  
J. P. King
Keyword(s):  
Power Series ◽  
Probability Distributions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Operators ◽  
Real Functions

Burmann series are used to give probability distributions which generalize the known class of distributions given by power series. Positive linear operators associated with Burmann-series distribution are described. Convergence of these operators to continuous real functions is studied. Examples are discussed.

The Orthogonal Polynomials of Power Series Probability Distributions and Their Uses

Biometrika ◽  
1966 ◽  
Vol 53 (1/2) ◽  
pp. 121
Author(s):  
D. F. I van Heerden ◽  
H. T. Gonin
Keyword(s):  
Power Series ◽  
Orthogonal Polynomials ◽  
Probability Distributions

scholarly journals From Invariance Under Binomial Thinning to Unification of the Cauchy and the Gołąb–Schinzel-Type Equations

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Karol Baron ◽  
Jacek Wesolowski
Keyword(s):  
Power Series ◽  
Functional Equations ◽  
Probability Distributions ◽  
Binomial Thinning ◽  
Additive Form

AbstractWe point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Gołąb–Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.

scholarly journals The T–R {Y} power series family of probability distributions

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Patrick Osatohanmwen ◽  
Francis O. Oyegue ◽  
Sunday M. Ogbonmwan
Keyword(s):  
Power Series ◽  
Probability Distributions

scholarly journals Max Weibull-G Power Series Distributions

2021 ◽  
pp. 15-29
Author(s):  
Munteanu Bogdan Gheorghe
Keyword(s):  
Probability Distribution ◽  
Power Series ◽  
Probability Distributions ◽  
Random Variables ◽  
Random Variable ◽  
Independent Random Variables ◽  
New Family ◽  
The Family ◽  
Distribution Family ◽  
Power Series Distributions

Based on the Weibull-G Power probability distribution family, we have proposed a new family of probability distributions, named by us the Max Weibull-G power series distributions, which may be applied in order to solve some reliability problems. This implies the fact that the Max Weibull-G power series is the distribution of a random variable max (X1 ,X2 ,...XN) where X1 ,X2 ,... are Weibull-G distributed independent random variables and N is a natural random variable the distribution of which belongs to the family of power series distribution. The main characteristics and properties of this distribution are analyzed.

scholarly journals A New Compound Lifetime Distribution: Model, Characterization, Estimation and Application

2018 ◽  
Vol 14 (2) ◽  
pp. 45-57
Author(s):  
Adil Rashid ◽  
Tariq Rashid Jan ◽  
Akhtar Hussain Bhat ◽  
Z. Ahmad
Keyword(s):  
Power Series ◽  
Probability Distributions ◽  
Distribution Model ◽  
Data Sets ◽  
Lifetime Data ◽  
Data Set ◽  
Power Series Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Random Events

Abstract There are diverse lifetime models available to the researchers to predict the uncertain behavior of random events but at times they fail to provide adequate fit for some complex and new data sets. New probability distributions are emerging as lifetime models to meet this ever growing demand of modeling complex real world phenomena from different sciences with better efficiency. Here, in this manuscript we shall compose Ailamujia distribution with that of power series distribution. This newly developed distribution called Ailamujia power series distribution reduces to four new special lifetime models on simple specific function parametric setting. Apart from this some important mathematical properties in the form of propositions will also be discussed. Furthermore, characterization and some statistical properties that include mgf, moments, and parameter estimation have also been discussed. Finally, the potency of newly proposed model has been analyzed statistically and graphically and it has been established from the statistical analysis that newly proposed model offers a better fit when it comes to model some lifetime data set.

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