scholarly journals Extending Singh-Maddala Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-23
Author(s):  
Mohammed Ali Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Real Data ◽  
Parameters Estimation ◽  
Random Numbers ◽  
Data Set ◽  
Mathematical Properties ◽  
New Distribution

A new distribution, the exponentiated transmuted Singh-Maddala distribution (ETSM), is presented, and three important special distributions are illustrated. Some mathematical properties are obtained, and parameters estimation method is applied using maximum likelihood. Illustrations based on random numbers and a real data set are given.

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 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 On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

scholarly journals SOME PROPERTIES OF BETA TRANSMUTED DAGUM DISTRIBUTION WITH APPLICATIONS

2020 ◽  
Vol 4 (2) ◽  
pp. 327-340
Author(s):  
Ahmed Ali Hurairah ◽  
Saeed A. Hassen
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Data Set ◽  
New Family ◽  
Method Of Maximum Likelihood ◽  
Dagum Distribution ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions called the beta transmuted Dagum distribution which extends the beta and transmuted familys. The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Dagum (BTD) distribution. The hazard function, moments, moment generating function, quantiles and stress-strength of the beta transmuted Dagum distribution (BTD) are provided and discussed in detail. The method of maximum likelihood estimation is used for estimating the model parameters. A simulation study is carried out to show the performance of the maximum likelihood estimate of parameters of the new distribution. The usefulness of the new model is illustrated through an application to a real data set.

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 On the Alpha Power Kumaraswamy Distribution: Properties, Simulation and Application

2020 ◽  
Vol 43 (2) ◽  
pp. 285-313
Author(s):  
Mohamed Ali Ahmed
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Simulation Studies ◽  
Data Set ◽  
Kumaraswamy Distribution ◽  
Mathematical Properties

Adding  new  parameters to  classical distributions becomes one  of  the most  important methods  for  increasing distributions flexibility,  especially, in  simulation   studies   and real data sets. In this paper, alpha power  transformation (APT) is used  and  applied  to  the Kumaraswamy (K) distribution and a proposed distribution, so called the alpha power Kumaraswamy (AK) distribution, is presented.  Some important mathematical properties are derived, parameters estimation of the AK distribution using maximum likelihood  method  is considered. A simulation study and  a  real  data   set  are  used  to  illustrate the  flexibility of the  AK distribution compared with other  distributions.

scholarly journals The Weibull Logistic-exponential Distribution: Its Properties and Applications

2020 ◽  
pp. 197-216
Author(s):  
I. U. Akata ◽  
J. E. Osemwenkhae
Keyword(s):  
Exponential Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Data Set ◽  
Lifetime Distributions ◽  
Mathematical Properties ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution ◽  
Generalized Distribution

In this paper, a new generalized distribution known as Weibull Logistic-Exponential Distribution (WLED) is proposed using the T-R{Y} framework. Several mathematical properties of this new distribution are studied. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit obtained by some comparable lifetime distributions.

The exponentiated exponential burr XII distribution: Theory and application to lifetime data

2020 ◽  
pp. 1-14
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Significant Heterogeneity ◽  
Lifetime Data ◽  
Fit Statistics ◽  
Mathematical Properties ◽  
New Distribution

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

Extended exponentiated Nadarajah-Haghighi model: Mathematical properties, characterizations and applications

2018 ◽  
Vol 55 (4) ◽  
pp. 498-522
Author(s):  
Morad Alizadeh ◽  
Mahdi Rasekhi ◽  
Haitham M. Yousof ◽  
Thiago G. Ramires ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Failure Rate Function ◽  
Data Set ◽  
Mathematical Properties

In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.

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