TRANSMUTED NORMAL DISTRIBUTION AND AN APPLICATION TO FINANCE

Abstract

Most of the statistical analyses are performed by using normal distribution theory such as regression analysis, hypothesis testing and analysis of variance. However, as indicated in many papers, in real life, nonnormal distributions are much more common than normal distribution. Therefore, the generalization of normal distribution has been widely studied in order to get more flexible fittings to real life data examples. In this paper, we generalize normal distribution by using quadratic rank transmution mapping method proposed by Shaw and Buckley [1]. Some properties like probability density function, cumulative distribution function and the moments of this new distribution are obtained. As an example, we applied this new proposed distribution to the Value at Risk (VaR) analysis which has been generally used in finance theory.