scholarly journals The Exponentiated Generalized-G Poisson Family of Distributions

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Gokarna R. Aryal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Real World ◽  
Generating Functions ◽  
Real World Data ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

AbstractIn this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

scholarly journals Inverse Odd Weibull Generated Family of Distribution

2020 ◽  
pp. 617-633 ◽  
Author(s):  
Joseph Thomas Eghwerido ◽  
John David Ikwuoche ◽  
Obinna Damian Adubisi
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Real Data ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Family ◽  
Mathematical Properties ◽  
The Family ◽  
Generated Family ◽  
Family Of Distributions

This work proposes an inverse odd Weibull (IOW) family of distributions for a lifetime distributions. Some mathematical properties of this family of distribution were derived. Survival, hazard, quantiles, reversed hazard, cumulative, odd functions, kurtosis, skewness, order statistics and entropies of this new family of distribution were examined. The parameters of the family of distributions were obtained by maximum likelihood. The behavior of the estimators were studied through simulation. The flexibility and importance of the distribution by means of real data set applications were emphasized.

The Marshall–Olkin Transmuted-G Family of Distributions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmed Z. Afify ◽  
Haitham M. Yousof ◽  
Morad Alizadeh ◽  
Indranil Ghosh ◽  
Samik Ray ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Statistics And Probability ◽  
Family Of Distributions

AbstractWe introduce a new family of univariate continuous distributions called the Marshall–Olkin transmuted-G family which extends the transmuted-G family pioneered by Shaw and Buckley (2007). Special models for the new family are provided. Some of its mathematical properties including quantile measure, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of two applications to real data sets.

scholarly journals On the Topp Leone Exponentiated-G Family of Distributions: Properties and Applications

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Sule Ibrahim ◽  
Sani Ibrahim Doguwa ◽  
Isah Audu ◽  
Jibril Haruna Muhammad
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Shape Parameters ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
Family Of Distributions

We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.

scholarly journals The Complementary Generalized Transmuted Poisson-G Family of Distributions

2018 ◽  
Vol 47 (4) ◽  
pp. 60-80 ◽  
Author(s):  
Morad Alizadeh ◽  
Haitham M. Yousof ◽  
Ahmed Z. Afify ◽  
Gauss M. Cordeiro ◽  
M. Mansoor
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Family Of Distributions

We introduce a new class of continuous distributions called the complementary generalized transmuted Poisson-G family, which extends the transmuted class pioneered by Shaw and Buckley (2007). We provide some special models and derive general mathematical properties including quantile function, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies and order statistics. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the new family is illustrated by means of two applications to real data sets.

scholarly journals Box-Cox Gamma-G Family of Distributions: Theory and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1801
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Maximum Likelihood ◽  
Statistical Model ◽  
Cauchy Distribution ◽  
Natural Generalization ◽  
Power Parameter ◽  
New Class ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Box Cox Transformation ◽  
Family Of Distributions

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.

scholarly journals General Results for the Transmuted Family of Distributions and New Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Marcelo Bourguignon ◽  
Indranil Ghosh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
New Models ◽  
Family Of Distributions

The transmuted family of distributions has been receiving increased attention over the last few years. For a baselineGdistribution, we derive a simple representation for the transmuted-Gfamily density function as a linear mixture of theGand exponentiated-Gdensities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.

scholarly journals The Weibull-G Poisson Family for Analyzing Lifetime Data

2020 ◽  
pp. 131-148 ◽  
Author(s):  
Haitham Yousof ◽  
Muhammad Mansoor ◽  
Morad Alizadeh ◽  
Ahmed Afify ◽  
Indranil Ghosh
Keyword(s):  
Generating Functions ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
New Family ◽  
Mathematical Properties ◽  
Independent Identically Distributed ◽  
Family Of Distributions

We study a new family of distributions defined by the minimum of the Poissonrandom number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of theproposed family.

The odd Nadarajah-Haghighi family of distributions: properties and applications

2019 ◽  
Vol 56 (2) ◽  
pp. 185-210 ◽  
Author(s):  
Abraão D. C. Nascimento ◽  
Kássio F. Silva ◽  
Gauss M. Cordeiro ◽  
Morad Alizadeh ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
New Family ◽  
Mathematical Properties ◽  
The Family ◽  
Family Of Distributions

Abstract We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of a real data set.

scholarly journals The Exponentiated Kumaraswamy-G Class: General Properties and Application

2019 ◽  
Vol 42 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Ronaldo Silva ◽  
Frank Gomes-Silva ◽  
Manoel Ramos ◽  
Gauss Moutinho Cordeiro ◽  
Pedro Marinho ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Weibull Model ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood

We propose a new family of distributions called the exponentiated Kumaraswamy-G class with three extra positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive some mathematical properties of the proposed class including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean deviations, reliability, Rényi entropy and Shannon entropy. The method of maximum likelihood is used to fit the distributions in the proposed class. Simulations are performed in order to assess the asymptotic behavior of the maximum likelihood estimates. We illustrate its potentiality with applications to two real data sets which show that the extended Weibull model in the new class provides a better fit than other generalized Weibull distributions.

scholarly journals The New rT - X Family of Distributions: Some Properties with Applications

2019 ◽  
pp. 409-432
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Data Sets ◽  
Statistical Distributions ◽  
Unknown Parameters ◽  
Related Data ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Modeling And Forecasting ◽  
Family Of Distributions

The rT - X family of distributions induced by V which have been introduced in [1] is further explored in this paper. In particular, we have obtained some basic mathematical properties of this new family. The simulation study shows the method of maximum likelihood is adequate in estimating the unknown parameters in sub-models of this new class of statistical distributions. Further, the application shows that sub-models of this new family of distributions are useful in material science engineering and related disciplines that call for modeling and forecasting of related data sets. Finally, inspired by the Ampadu-G family of distributions [2], we propose a new class of distributions that have never appeared in the literature, and ask the reader to investigate some properties and applications of this new class of distributions.

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