scholarly journals The Beta Generalized Half-Normal Distribution: New Properties

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Gauss M. Cordeiro ◽  
Rodrigo R. Pescim ◽  
Edwin M. M. Ortega ◽  
Clarice G. B. Demétrio
Keyword(s):  
Normal Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Positive Real ◽  
Lorenz Curves ◽  
Statistical Measures ◽  
Method Of Maximum Likelihood ◽  
Useful Power

We study some mathematical properties of the beta generalized half-normal distribution recently proposed by Pescim et al. (2010). This model is quite flexible for analyzing positive real data since it contains as special models the half-normal, exponentiated half-normal, and generalized half-normal distributions. We provide a useful power series for the quantile function. Some new explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability, and entropy. We demonstrate that the density function of the beta generalized half-normal order statistics can be expressed as a mixture of generalized half-normal densities. We obtain two closed-form expressions for their moments and other statistical measures. The method of maximum likelihood is used to estimate the model parameters censored data. The beta generalized half-normal model is modified to cope with long-term survivors may be present in the data. The usefulness of this distribution is illustrated in the analysis of four real data sets.

scholarly journals Odd Lomax-Kumaraswamy Distribution: Its Properties and Applications

2020 ◽  
pp. 45-60
Author(s):  
Bassa Shiwaye Yakura ◽  
Ahmed Askira Sule ◽  
Mustapha Mohammed Dewu ◽  
Kabiru Ahmed Manju ◽  
Fadimatu Bawuro Mohammed
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Model Parameters ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

This article uses the odd Lomax-G family of distributions to study a new extension of the Kumaraswamy distribution called “odd Lomax-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lomax-Kumaraswamy distribution are defined and studied with many other properties of the distribution such as the ordinary moments, moment generating function, characteristic function, quantile function, reliability functions, order statistics and other useful measures. The model parameters are estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real data sets.

scholarly journals A New Generalized Log-logistic and Modified Weibull Distribution with Applications

2018 ◽  
Vol 7 (3) ◽  
pp. 72
Author(s):  
Broderick O. Oluyede ◽  
Huybrechts F. Bindele ◽  
Boikanyo Makubate ◽  
Shujiao Huang
Keyword(s):  
Hazard Function ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
Method Of Maximum Likelihood ◽  
Special Cases ◽  
L Moments ◽  
Modified Weibull

A new generalized distribution called the {\em log-logistic modified Weibull} (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and R\'enyi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals The Nadarajah Haghighi Topp Leone-G Family of Distributions ‎with Mathematical Properties and Applications

2019 ◽  
Vol 15 (4) ◽  
pp. 849
Author(s):  
Hesham Reyad‎ ◽  
Mahmoud Ali Selim ◽  
Soha Othman
Keyword(s):  
Information Matrix ◽  
Quantile Function ◽  
Model Parameters ◽  
Lorenz Curves ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Statistics And Probability ◽  
Method Of Maximum Likelihood

Based on the Nadarajah Haghighi distribution and the Topp Leone-G family in view of the T-X family, we introduce a new generator of continuous distributions with three extra parameters called the Nadarajah Haghighi Topp Leone-G family. Three sub-models of the new class are discussed. Main mathematical properties of the new family are investigated such as; quantile function, raw and incomplete moments, Bonferroni and Lorenz curves, moment and probability generating functions, stress-strength model, Shanon and Rényi entropies, order statistics and probability weighted moments. The model parameters of the new family is estimated by using the method of maximum likelihood and the observed information matrix is also obtained. We introduce two real applications to show the importance of the new family.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals On the Extended Generalized Inverse Exponential Distribution with Its Applications

2020 ◽  
pp. 14-27
Author(s):  
Sule Ibrahim ◽  
Bello Olalekan Akanji ◽  
Lawal Hammed Olanrewaju
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Generalized Inverse ◽  
Real Data ◽  
Quantile Function ◽  
Exponential Model ◽  
Data Sets ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Exponential Distribution

We propose a new distribution called the extended generalized inverse exponential distribution with four positive parameters, which extends the generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate and odd functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to two real data sets which show that the extended generalized inverse exponential model provides a better fit than other models considered.

scholarly journals The Log-logistic Weibull Distribution with Applications to Lifetime Data

2016 ◽  
Vol 45 (3) ◽  
pp. 43-69 ◽  
Author(s):  
Broderick Oluyede ◽  
Susan Foya ◽  
Gayan Warahena-Liyanage ◽  
Shujiao Huang
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
Method Of Maximum Likelihood ◽  
L Moments ◽  
New Distribution ◽  
Generalized Distribution ◽  
Func Tion

In this paper, a new generalized distribution called the log-logisticWeibull (LLoGW) distribution is developed and presented. This dis-tribution contain the log-logistic Rayleigh (LLoGR), log-logistic expo-nential (LLoGE) and log-logistic (LLoG) distributions as special cases.The structural properties of the distribution including the hazard func-tion, reverse hazard function, quantile function, probability weightedmoments, moments, conditional moments, mean deviations, Bonferroniand Lorenz curves, distribution of order statistics, L-moments and Renyientropy are derived. Method of maximum likelihood is used to estimatethe parameters of this new distribution. A simulation study to examinethe bias, mean square error of the maximum likelihood estimators andwidth of the condence intervals for each parameter is presented. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

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 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 odd flexible Weibull-H family of distributions: Properties and estimation with applications to complete and upper record data

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2635-2652 ◽  
Author(s):  
M. El-Morshedy ◽  
M.S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Lorenz Curves ◽  
New Family ◽  
Record Data ◽  
Upper Record

In this paper, a new generator of continuous distributions called the odd flexible Weibull-H family is proposed and studied. Some of its statistical properties including quantile, skewness, kurtosis, hazard rate function, moments, incomplete moments, mean deviations, coefficient of variation, Bonferroni and Lorenz curves, moments of the residual (past) lifetimes and entropies are studied. Two special models are introduced and discussed in-detail. The maximum likelihood method is used to estimate the model parameters based on complete and upper record data. Adetailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, three applications to real data sets show the flexibility of the new family.

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