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.

scholarly journals Transmuted Probability Distributions: A Review

2020 ◽  
pp. 83-94
Author(s):  
Md. Mahabubur Rahman ◽  
Bander Al-Zahrani ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Functional Composition ◽  
Inverse Cumulative Distribution Function ◽  
Family Of Distributions

Transmutation is the functional composition of the cumulative distribution function (cdf) of one distribution with the inverse cumulative distribution function (quantile function) of another. Shaw and Buckley(2007), first apply this concept and introduced quadratic transmuted family of distributions. In this article, we have presented a review about the transmuted families of distributions. We have also listed the transmuted distributions, available in the literature along with some concluding remarks.

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 On a New Result on the Ratio Exponentiated General Family of Distributions with Applications

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 598 ◽  
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Natural Extension ◽  
Continuous Distribution ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Model Parameters ◽  
Mathematical Treatment ◽  
General Family ◽  
Family Of Distributions

In this paper, we first show a new probability result which can be concisely formulated as follows: the function 2 G β / ( 1 + G α ) , where G denotes a baseline cumulative distribution function of a continuous distribution, can have the properties of a cumulative distribution function beyond the standard assumptions on α and β (possibly different and negative, among others). Then, we provide a complete mathematical treatment of the corresponding family of distributions, called the ratio exponentiated general family. To link it with the existing literature, it constitutes a natural extension of the type II half logistic-G family or, from another point of view, a compromise between the so-called exponentiated-G and Marshall-Olkin-G families. We show that it possesses tractable probability functions, desirable stochastic ordering properties and simple analytical expressions for the moments, among others. Also, it reaches high levels of flexibility in a wide statistical sense, mainly thanks to the wide ranges of possible values for α and β and thus, can be used quite effectively for the real data analysis. We illustrate this last point by considering the Weibull distribution as baseline and three practical data sets, with estimation of the model parameters by the maximum likelihood method.

scholarly journals A New Power Topp–Leone Generated Family of Distributions with Applications

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1177
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Real Life ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Model Parameters ◽  
Full Generality ◽  
New Family ◽  
Inverse Lomax Distribution ◽  
Family Of Distributions

In this paper, we introduce a new general family of distributions obtained by a subtle combination of two well-established families of distributions: the so-called power Topp–Leone-G and inverse exponential-G families. Its definition is centered around an original cumulative distribution function involving exponential and polynomial functions. Some desirable theoretical properties of the new family are discussed in full generality, with comprehensive results on stochastic ordering, quantile function and related measures, general moments and related measures, and the Shannon entropy. Then, a statistical parametric model is constructed from a special member of the family, defined with the use of the inverse Lomax distribution as the baseline distribution. The maximum likelihood method was applied to estimate the unknown model parameters. From the general theory of this method, the asymptotic confidence intervals of these parameters were deduced. A simulation study was conducted to evaluate the numerical behavior of the estimates we obtained. Finally, in order to highlight the practical perspectives of the new family, two real-life data sets were analyzed. All the measures considered are favorable to the new model in comparison to four serious competitors.

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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