Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study

2010 ◽  
Vol 26 (1) ◽  
pp. 31-54 ◽  
Author(s):  
Gregor Weiß
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Minimum Distance ◽  
Copula Parameter ◽  
Minimum Distance Estimators

scholarly journals Estimating the Gumbel-Barnett copula parameter of dependence

2018 ◽  
Vol 41 (1) ◽  
pp. 53-73 ◽  
Author(s):  
Jennyfer Portilla Yela ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Empirical Evaluation ◽  
Bayesian Estimator ◽  
Dependence Structure ◽  
Type I ◽  
Copula Parameter

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

scholarly journals On Zero-Modified Poisson-Sujatha Distribution to Model Overdispersed Count Data

2018 ◽  
Vol 47 (3) ◽  
pp. 1-19
Author(s):  
Wesley Bertoli Da Silva ◽  
Angélica Maria Tortola Ribeiro ◽  
Katiane Silva Conceição ◽  
Marinho Gomes Andrade ◽  
Francisco Louzada Neto
Keyword(s):  
Biological Sciences ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Count Data ◽  
Probability Function ◽  
Hurdle Model ◽  
Asymptotic Inference ◽  
Proposed Model

In this paper we propose the zero-modified Poisson-Sujatha distribution as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. It will be shown that the zero modification can be incorporated by using the zero-truncated Poisson-Sujatha distribution. A simple reparametrization of the probability function will allow us to represent the zero-modified Poisson-Sujatha distribution as a hurdle model. This trick leads to the fact that proposed model can be fitted without any previously information about the zero modification present in a given dataset. The maximum likelihood theory will be used for parameter estimation and asymptotic inference concerns. A simulation study will be conducted in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed model will be illustrated using real datasets of the biological sciences field and comparing it with other models available in the literature.

scholarly journals The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248873
Author(s):  
Majdah Badr ◽  
Muhammad Ijaz
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Probability Distribution ◽  
Simulation Study ◽  
Probability Distributions ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Lifetime Data ◽  
Confidence Bounds

The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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