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.

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 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 Beta Log-Logistic Weibull Distribution: Model, Properties and Application

2018 ◽  
Vol 7 (6) ◽  
pp. 49
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Neo Dingalo ◽  
Adeniyi Francis Fagbamigbe
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Maximum Likelihood Estimates ◽  
Distribution Model ◽  
Monte Carlo Simulation Study ◽  
Special Cases ◽  
Generalized Distribution

We propose and develop the properties of a new generalized distribution called the beta log-logistic Weibull (BLLoGW) distribution. This model contain several new distributions such as beta log-logistic Rayleigh, beta log-logistic exponential, exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential,  log-logistic Weibull, log-logistic Rayleigh and log-logistic distributions as special cases. Structural properties of this generalized distribution including series expansion of the probability density function and cumulative distribution function, hazard function, reverse hazard function, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, R\'enyi entropy and distribution of order statistics are presented. The parameters of the distribution are estimated using maximum likelihood estimation technique. A Monte Carlo simulation study is conducted to examine the bias and mean square error of the maximum likelihood estimates. A real dataset is used to illustrate the applicability and usefulness of the new generalized distribution.

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 Gompertz Gumbel II Distribution: Properties and Applications

2020 ◽  
pp. 1-15
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Donatus Osaretin Omosigho
Keyword(s):  
Real Life ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Life Data ◽  
Real Life Data ◽  
Decreasing Failure Rate ◽  
New Distribution

In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

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 Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Maha A. Aldahlan
Keyword(s):  
Maximum Likelihood Method ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Alpha Power ◽  
New Model ◽  
Mathematical Properties

In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.

scholarly journals A Lomax-inverse Lindley Distribution: Model, Properties and Applications to Lifetime Data

2019 ◽  
pp. 1-28
Author(s):  
Terna Godfrey Ieren ◽  
Peter Oluwaseun Koleoso ◽  
Adana’a Felix Chama ◽  
Innocent Boyle Eraikhuemen ◽  
Nasiru Yakubu
Keyword(s):  
Likelihood Estimation ◽  
Quantile Function ◽  
Distribution Model ◽  
Lindley Distribution ◽  
Limiting Behavior ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Lindley Distribution ◽  
New Distribution ◽  
Better Than

This article proposed a new extension of the Inverse Lindley distribution called “Lomax-Inverse Lindley distribution” which is more flexible compared to the Inverse Lindley distribution and other similar models. The paper derives and discusses some Statistical properties of the new distribution which include the limiting behavior, quantile function, reliability functions and distribution of order statistics. The parameters of the new model are estimated by method of maximum likelihood estimation. Conclusively, three lifetime datasets were used to evaluate the usefulness of the proposed model and the results indicate that the proposed extension is more flexible and performs better than the other distributions considered in this study.

scholarly journals An Extension of Log-Logistic Distribution for Analyzing Survival Data

2020 ◽  
pp. 789-801
Author(s):  
Aliya Syed Malik ◽  
S.P. Ahmad
Keyword(s):  
Survival Data ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Logistic Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

scholarly journals The Kumaraswamy Pareto IV Distribution

2021 ◽  
Vol 50 (5) ◽  
pp. 1-22
Author(s):  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Muhammad Mansoor ◽  
Muhammad Zubair ◽  
Ayman Alzaatreh
Keyword(s):  
Density Function ◽  
Residual Life ◽  
Information Matrix ◽  
Real Life ◽  
Quantile Function ◽  
Mean Residual Life ◽  
Model Parameters ◽  
New Model ◽  
Lorenz Curves ◽  
Mean Waiting Time

We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.

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