Numerical and Monte Carlo Methods to make Normal Residues in Regression

The Jarque-Bera normality test verifies if the residues of the regression hyper-plane are normal random variables.In this paper we present some numerical and Monte Carlo methods to obtain normal residues if the Jarque-Bera test fails. We consider the case when we know the pdf, the cdf and the inverse of the cdf for the random variable Y (example: the exponential distribution), the case when we know only the first two elements (example: Erlang distribution) and the case when we know only the pdf (example: the gamma distribution). We consider also the case when we do not know even an analytical formula for the pdf. In this case we will estimate the pdf using some known kernels (see section 2).