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.

Bayesian Survival Analysis for Generalized Pareto Distribution Under Progressively Type II Censored Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050001
Author(s):  
Shaowei Li ◽  
Wenhao Gui
Keyword(s):  
Pareto Distribution ◽  
Survival Function ◽  
Information Matrix ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Point Estimate ◽  
Type Ii ◽  
Nonparametric Bootstrap ◽  
Monte Carlo Simulation Study ◽  
Generalized Pareto

In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented.

scholarly journals Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation

2020 ◽  
pp. 21-33 ◽  
Author(s):  
Hanan Haj AHmad ◽  
Ehab Almetwally
Keyword(s):  
Loss Function ◽  
Bayesian Method ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type I ◽  
Generalized Pareto

A new generalization of generalized Pareto Distribution is obtained using the generator Marshall-Olkin distribution (1997). The new distribution MOGP is more flexible and can be used to model non-monotonic failure rate functions. MOGP includes six different sub models: Generalized Pareto, Exponential, Uniform, Pareto type I, Marshall-Olkin Pareto and Marshall-Olkin exponential distribution. We consider different estimation procedures for estimating the model parameters, namely: Maximum likelihood estimator, Maximum product spacing, Least square method, weighted least square method and Bayesian Method. The Bayesian Method is considered under quadratic loss function and Linex loss function. Simulation analysis using MCMC technique is performed to compare between the proposed point estimation methods. The usefulness of MOGP is illustrated by means of real data set, which shows that this generalization is better fit than Pareto, GP and MOP 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 Performance-based comparison of regionalization methods to improve the at-site estimates of daily precipitation

2021 ◽  
Author(s):  
Abubakar Haruna ◽  
Juliette Blanchet ◽  
Anne-Catherine Favre
Keyword(s):  
Pareto Distribution ◽  
Daily Precipitation ◽  
Additive Model ◽  
Generalized Pareto Distribution ◽  
Regional Frequency Analysis ◽  
Distribution Model ◽  
Model Parameters ◽  
Generalized Pareto ◽  
Spatial Method ◽  
Homogeneous Regions

Abstract. In this article, we compare the performances of three regionalization approaches in improving the at-site estimates of daily precipitation. The first method is built on the idea of conventional RFA (Regional Frequency Analysis) but is based on a fast algorithm that defines distinct homogeneous regions relying on their upper tail similarity. It uses only the precipitation data at hand without the need for any additional covariate. The second is based on the region-of-influence (ROI) approach in which neighborhoods, containing similar sites, are defined for each station. The third is a spatial method that adopts Generalized Additive Model (GAM) forms for the model parameters. In line with our goal of modeling the whole range of positive precipitation, the chosen marginal distribution model is the Extended Generalized Pareto Distribution (EGPD) on which we apply the three methods. We consider a dense network composed of 1176 daily stations located within Switzerland and in neighboring countries. We compute different criteria to assess the models' performances both in the bulk of the distribution as well as in the upper tail. The results show that all the regional methods offered improved robustness over the local EGPD model. While the GAM method is more robust and reliable in the upper tail, the ROI method is better in the bulk of the distribution.

scholarly journals On the Properties of the New Generalized Pareto Distribution and Its Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Najma Salahuddin ◽  
Alamgir Khalil ◽  
Wali Khan Mashwani ◽  
Sharifah Alrajhi ◽  
Sanaa Al-Marzouki ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Mean Squared Error ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Parametric Estimation ◽  
Maximum Likelihood Estimates ◽  
Suggested Model ◽  
Practical Applications ◽  
Generalized Pareto

In this paper, a new generalization of the Generalized Pareto distribution is proposed using the generator suggested in [1], named as Khalil Extended Generalized Pareto (KEGP) distribution. Various shapes of the suggested model and important mathematical properties are investigated that includes moments, quantile function, moment-generating function, measures of entropy, and order statistics. Parametric estimation of the model is discussed using the technique of maximum likelihood. A simulation study is performed for the assessment of the maximum likelihood estimates in terms of their bias and mean squared error using simulated sample estimates. The practical applications are illustrated via two real data sets from survival and reliability theory. The suggested model provided better fits than the other considered models.

scholarly journals Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Rashad M. El-Sagheer ◽  
Taghreed M. Jawa ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Pareto Distribution ◽  
Confidence Region ◽  
Generalized Pareto Distribution ◽  
Simulated Data ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Failure Data ◽  
Generalized Pareto

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.

scholarly journals The Burr-Weibull Power Series Class of Distributions

2018 ◽  
Vol 48 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Broderick Oluyede ◽  
Precious Mdlongwa ◽  
Boikanyo Makubate ◽  
Shujiao Huang
Keyword(s):  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Estimation Technique ◽  
Exponential Distributions ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Special Model ◽  
Mathematical Properties

A new generalized class of distributions called the Burr-Weibull Power Series (BWPS) class of distributions is developed and explored. This class of distributions generalizes the Burr power series and Weibull power series classes of distributions, respectively. A special model of the BWPS class of distributions, the new Burr-Weibull Poisson (BWP) distribution is considered and some of its mathematical properties are obtained. The BWP distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential Poisson, Burr-exponential, Burr-Rayleigh Poisson, Burr-Rayleigh, Burr-Poisson, Burr, Lomax-exponential Poisson, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax-Poisson, Lomax, Weibull, Rayleigh and exponential distributions. Maximum likelihood estimation technique is used to estimate the model parameters followed by a Monte Carlo simulation study. Finally an application of the BWP model to a real data set is presented to illustrate the usefulness of the proposed class of distributions.

scholarly journals Another Generalized Transmuted family of distributions:Properties and Applications

2016 ◽  
Vol 45 (3) ◽  
pp. 71-93 ◽  
Author(s):  
Faton Merovci ◽  
Morad Alizadeh ◽  
G. G Hamedani
Keyword(s):  
Generating Functions ◽  
Extreme Values ◽  
Real Data ◽  
Model Parameters ◽  
Likelihood Estimator ◽  
Baseline Model ◽  
Lorenz Curves ◽  
New Family ◽  
Mathematical Properties ◽  
The Family

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution.  We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we introduce a bivariate extensions of the new family. We discuss the different method of estimation of the model parameters  and illustrate the potentiality of the family by means of two applications to real data. A brief simulation for evaluating Maximum likelihood estimator is done.

scholarly journals The Exponentiated Half-Logistic Family of Distributions: Properties and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Morad Alizadeh ◽  
Edwin M. M. Ortega
Keyword(s):  
Real Data ◽  
Rate Function ◽  
Model Parameters ◽  
Data Sets ◽  
Baseline Model ◽  
Lorenz Curves ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Logistic Family

We study some mathematical properties of a new generator of continuous distributions with two extra parameters called the exponentiated half-logistic family. We present some special models. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, and order statistics, which hold for any baseline model. We introduce two bivariate extensions of this family. We discuss the estimation of the model parameters by maximum likelihood and demonstrate the potentiality of the new family by means of two real data sets.

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