# The Use of Non-Parametric Methods to Estimate Density Functions of Copulas

#### Authors:

Munaf Yousif Hmood,Zainab Falih Hamza,

#### DOI NO:

https://doi.org/10.26782/jmcms.2019.08.00040

#### Keywords:

Copula functions,Transformation kernel,Beta kernel,LocalLikelihood transformation Estimator,

#### Abstract

Copulas distinguish the dependence among random vectors components as opposed to marginal and joint distributions, which can be directly observed, thus,so the copulas are considered as a hidden dependence among random vectors. Hence , the copulas could be defined as a structure that connects the joint distribution with the marginal distribution based on the non-parametric estimation with the use of the kernel function by the existence of the copula as it is considered as a tool hugely used in the modern statistics and more used in the non-parametric estimations; besides indicating the general characteristics of the estimator and selecting the appropriate bandwidth through the simulation process. A comparison was carried out between transformation estimator and Beta estimator and local likelihood transformation(LLTE) estimator in the estimation of the probability density function , using bimodel normal distribution. The results of simulation showed , according to the measurement of comparison used , that the best method is the method of (LLTE), where V. good estimations and easily to be implemented have been obtained while reducing boundary effect problems.

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