scholarly journals The Zeta-G Class: Some Computational and Analytical Aspects

2020 ◽  
Vol 42 ◽  
pp. e111
Author(s):  
Ana Carla Percontini ◽  
Frank Gomes-Silva ◽  
Gauss Moutinho Crdeiro ◽  
Pedro Rafael Marinho
Keyword(s):  
Maximum Likelihood ◽  
Generating Function ◽  
Real Data ◽  
Data Set ◽  
R Language ◽  
New Class ◽  
Mathematical Properties ◽  
Special Cases ◽  
Computational Aspects

We define a new class of distributions with one extra shapeparameter including some special cases. We provide numerical and computational aspects of the new class. We proposefunctions using the \textsf{R} language to fit any distribution in this family to a data set. In addition, such functions are implemented efficientlyusing the library \textsf{Rcpp} that enables the incorporation of the codes \textsf{C++} in \textsf{R} automatically. Some examples are presentedfor using the implemented routines in practice. We derive some mathematical properties of this class including explicit expressionsfor the moments, generating function and mean deviations. We discuss the estimation of the model parametersby maximum likelihood and provide an application to a real data set.

scholarly journals A New Extended-F Family: Properties and Applications to Lifetime Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Saima K. Khosa ◽  
Ahmed Z. Afify ◽  
Zubair Ahmad ◽  
Mi Zichuan ◽  
Saddam Hussain ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Model Parameters ◽  
Additional Parameter ◽  
Alpha Power ◽  
New Approach ◽  
New Class ◽  
Mathematical Properties ◽  
Extended Weibull Distribution

In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as a special submodel of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived, and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data, and the comparison is made with the Weibull and some of its well-known extensions such as Marshall–Olkin Weibull, alpha power-transformed Weibull, and Kumaraswamy Weibull distributions.

scholarly journals The Gumbel- Pareto Distribution: Theory and Applications

2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Numerical Illustration ◽  
Data Set ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
First Time ◽  
New Distribution

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

scholarly journals The Beta Weibull-G Family of Distributions: Model, Properties and Application

2018 ◽  
Vol 7 (2) ◽  
pp. 12 ◽  
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Gofaone Motobetso ◽  
Shujiao Huang ◽  
Adeniyi F. Fagbamigbe
Keyword(s):  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Generalized Distributions ◽  
Special Cases

A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series expansion of the density function, hazard function, moments, mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates of the model parameters are given. Application of the model to real data set is presented to illustrate the importance and usefulness of the special case beta Weibull-log-logistic distribution.

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 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 A New Generalized Family of Odd Lindley-G Distributions With Application

2019 ◽  
Vol 8 (6) ◽  
pp. 1
Author(s):  
Fastel Chipepa ◽  
Broderick O. Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Hazard Rate ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Lorenz Curves ◽  
New Family ◽  
Special Cases ◽  
Family Of Distributions

A new family of distributions, namely the Kumaraswamy Odd Lindley-G distribution is developed. The new density function can be expressed as a linear combination of exponentiated-G densities. Statistical properties of the new family including hazard rate and quantile functions, moments and incomplete moments, Bonferroni and Lorenz curves, distribution of order statistics and R´enyi entropy are derived. Some special cases are presented. We conduct some Monte Carlo simulations to examine the consistency of the maximum likelihood estimates. We provide an application of KOL-LLo distribution to a real data set.

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 A New Class of Generalized Modified Weibull Distribution with Applications

2015 ◽  
Vol 44 (3) ◽  
pp. 45-68
Author(s):  
Broderick Oluyede ◽  
Shujiao Huang ◽  
Tiantian Yang
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Estimation Technique ◽  
Exponential Distributions ◽  
New Class ◽  
Mathematical Properties ◽  
Special Cases ◽  
Generalized Modified Weibull ◽  
Modified Weibull

A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

scholarly journals An Extension of the Kumaraswamy Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 61
Author(s):  
Jalmar M. F. Carrasco ◽  
Gauss M Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Integral Transform ◽  
Continuous Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution ◽  
Special Cases ◽  
The Impact ◽  
Parameter Constraints

We propose and study a new five-parameter continuous distribution in the unit interval through a specific probability integral transform. The new distribution, under some parameter constraints, is an identified parametric model that includes as special cases six important models such as the Kumaraswamy and beta distributions. We obtain ordinary and incomplete moments, quantile and generating functions, mean deviations, R\'enyi entropy and moments of order statistics. The estimation of the model parameters is performed by maximum likelihood, and hypothesis tests are discussed. Additionally, through a simulation study we investigate the behavior of the maximum likelihood estimator, also we investigate the impact of ignoring identifiability problems. The usefulness of the proposed distribution is illustrated by means of a real data set.

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