scholarly journals On the Generalized Lognormal Distribution

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Thomas L. Toulias ◽  
Christos P. Kitsos
Keyword(s):  
Distribution Function ◽  
Uniform Distribution ◽  
Series Expansion ◽  
Lognormal Distribution ◽  
Cumulative Distribution Function ◽  
Shape Parameter ◽  
Error Function ◽  
Cumulative Distribution ◽  
Dirac Distribution

This paper introduces, investigates, and discusses the -order generalized lognormal distribution (-GLD). Under certain values of the extra shape parameter , the usual lognormal, log-Laplace, and log-uniform distribution, are obtained, as well as the degenerate Dirac distribution. The shape of all the members of the -GLD family is extensively discussed. The cumulative distribution function is evaluated through the generalized error function, while series expansion forms are derived. Moreover, the moments for the -GLD are also studied.

scholarly journals New handy and accurate approximation for the Gaussian integrals with applications to science and engineering

2019 ◽  
Vol 17 (1) ◽  
pp. 1774-1793 ◽  
Author(s):  
Mario A. Sandoval-Hernandez ◽  
Hector Vazquez-Leal ◽  
Uriel Filobello-Nino ◽  
Luis Hernandez-Martinez
Keyword(s):  
Distribution Function ◽  
Power Series ◽  
Cumulative Distribution Function ◽  
Error Function ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Cumulative Distribution ◽  
Accurate Approximation ◽  
Science And Engineering ◽  
Gaussian Integral

Abstract In this work, we propose to approximate the Gaussian integral, the error function and the cumulative distribution function by using the power series extender method (PSEM). The approximations proposed in this paper present a high accuracy for the complete domain [–∞,∞]. Furthermore, the approximations are handy and easy computable, avoiding the application of special numerical algorithms. In order to show its high accuracy, three case studies are presented with applications to science and engineering.

scholarly journals Statistical Inference for a General Family of Modified Exponentiated Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3069
Author(s):  
Emilio Gómez-Déniz ◽  
Yuri A. Iriarte ◽  
Yolanda M. Gómez ◽  
Inmaculada Barranco-Chamorro ◽  
Héctor W. Gómez
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Shape Parameter ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Tail Behavior ◽  
Poisson Mixture ◽  
Mixing Distribution ◽  
Family Of Distributions

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile function, moments, stochastic ordering, Poisson mixture with our proposal as the mixing distribution, order statistics, tail behavior and estimates of parameters. We highlight the particular model based on the classical exponential distribution, which is an alternative to the exponentiated exponential, gamma and Weibull. A simulation study and a real application are presented. It is shown that the proposed family of distributions is of interest to applied areas, such as economics, reliability and finances.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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