Bivariate Lorenz Curves Based on the Sarmanov–Lee Distribution

2014 ◽  
pp. 447-455 ◽  
Author(s):  
José María Sarabia ◽  
Vanesa Jordá
Keyword(s):  
Lorenz Curves

A CLASS OF LORENZ CURVES BASED ON LINEAR EXPONENTIAL LOSS FUNCTIONS

2002 ◽  
Vol 31 (6) ◽  
pp. 925-942 ◽  
Author(s):  
José María Sarabia ◽  
Marta Pascual
Keyword(s):  
Loss Functions ◽  
Lorenz Curves

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 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.

scholarly journals Quantum relative Lorenz curves

2017 ◽  
Vol 95 (1) ◽  
Author(s):  
Francesco Buscemi ◽  
Gilad Gour
Keyword(s):  
Lorenz Curves

Anything Lorenz Curves Can Do, Top Shares Can Do: Assessing the TopBot Family of Inequality Measures

2018 ◽  
Vol 49 (4) ◽  
pp. 947-981 ◽  
Author(s):  
Guillermina Jasso
Keyword(s):  
Gini Coefficient ◽  
Probability Distributions ◽  
The United States ◽  
Current Evidence ◽  
Inequality Measure ◽  
Lorenz Curves ◽  
Inequality Measures ◽  
Top Incomes ◽  
The Gini Coefficient ◽  
And Shifts

Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People’s measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.

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