Copula modeling is widely used in modern statistics. The boundary bias problem is one of the problems faced when estimating by nonparametric methods, as kernel estimators are the most common in nonparametric estimation. In this paper, the copula density function was estimated using the probit transformation nonparametric method in order to get rid of the boundary bias problem that the kernel estimators suffer from. Using simulation for three nonparametric methods to estimate the copula density function and we proposed a new method that is better than the rest of the methods by five types of copulas with different sample sizes and different levels of correlation between the copula variables and the different parameters for the function. The results showed that the best method is to combine probit transformation and mirror reflection kernel estimator (PTMRKE) and followed by the (IPE) method when using all copula functions and for all sample sizes if the correlation is strong (positive or negative). But in the case of using weak and medium correlations, it turns out that the (IPE) method is the best, followed by the proposed method(PTMRKE), depending on (RMSE, LOGL, Akaike)criteria. The results also indicated that the mirror kernel reflection method when using the five copulas is weak.
Probit and Improved Probit Transform-Based Kernel Estimator for
Copula Density
Copula function
Probit transformation
Kernel copula function
Improved probit transformation
Mirror reflection
Boundary bias
Publication Date
Mon Nov 01 2010
Journal Name
Al-nahrain Journal Of Science
Chemical Elements Diffusion in the Solar Interior
The standard solar model and equation of state have been used to study relative diffusion of Hydrogen and Helium in the present time for solar interior
as a function of distance and depth from the center of the star. The effects of temperature and density on diffusion velocity for these chemical elements have been explaned.
It is found that heat flow which is arising from these reactions leads to an increase in helium diffusion velocity
while the temperature and density leading to a decrease in Hydrogen diffusion velocity. This means that Hydrogen behaves inversely with that for helium does through these reactions. Accordingly
diffusion percentages for Hydrogen
Helium and other Heavy Elements could be determined for the main sequence stars and white dwarf stars.