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.

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.

A New Gamma Generalized Lindley-Log- logistic Distribution with Applications

2020 ◽  
Vol 15 (4) ◽  
pp. 2451-2479
Author(s):  
Broderick Olusegun Oluyede ◽  
Thatayaone Moakofi ◽  
Boikanyo Makubate
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
New Distribution

A new distribution called the gamma exponentiated Lindley Log-logistic (GELLLoG) distribution is developed. Some properties of the new distribution including hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Réenyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. We conduct a simulation study to examine the bias and mean square error of the maximum likelihood estimators. Finally, applications to real datasets to illustrate the usefulness of the proposed distribution are presented.

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.

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 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 The Odd Lindley-G Family of Distributions

2017 ◽  
Vol 46 (1) ◽  
pp. 65-87 ◽  
Author(s):  
Frank S. Gomes-Silva ◽  
Ana Percontini ◽  
Edleide de Brito ◽  
Manoel W. Ramos ◽  
Ronaldo Venâncio ◽  
...  
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Record Values ◽  
Model Parameters ◽  
Baseline Model ◽  
Data Set ◽  
New Family ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record

We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Renyi entropy, reliability, order statistics and their moments and k upper record values. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.

scholarly journals The Beta Transmuted Weibull Distribution

2014 ◽  
Vol 43 (2) ◽  
pp. 133-149 ◽  
Author(s):  
Manisha Pal ◽  
Montip Tiensuwan
Keyword(s):  
Weibull Distribution ◽  
Censored Data ◽  
Weibull Model ◽  
Model Parameters ◽  
Lorenz Curves ◽  
Positive Data ◽  
Method Of Maximum Likelihood ◽  
Special Cases ◽  
The Mean ◽  
New Distribution

The paper introduces a beta transmuted Weibull distribution, which contains a number ofdistributions as special cases. The properties of the distribution are discussed and explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, and reliability. The distribution and moments of order statistics are also studied. Estimation of the model parameters by the method of maximum likelihood is discussed. The log beta transmuted Weibull model is introduced to analyze censored data. Finally, the usefulness of the new distribution in analyzing positive data is illustrated.

Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications

2021 ◽  
Vol 71 (5) ◽  
pp. 1269-1290
Author(s):  
Thatayaone Moakofi ◽  
Broderick Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Hazard Function ◽  
Real Life ◽  
Quantile Function ◽  
Distribution Model ◽  
Logistic Distribution ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
New Distribution ◽  
Generalized Distribution

Abstract The authors introduce a new generalized distribution called the Marshall-Olkin Lindley-Log-logistic (MOLLLoG) distribution and discuss its distributional properties. The properties include hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Rényi entropy. A Monte Carlo simulation study was used to examine the bias, relative bias and mean square error of the maximum likelihood estimators. The betterness of the new distribution compared to other distributions is illustrated by means of two real life datasets.

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

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