The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters

Recently, in the area of finance, especially for the risk management, some heavy-tailed and skewed distributions are strongly required. The Pearson type IV distribution can represent various kurtosis and skewness. However, it has not been used for practical purpose because of the difficulties of its implementation. This paper discusses the practical methods which could overcome various difficulties involved. Type IV is defined explicitly by the "skewed version" of type VII. The general normalizing constant is newly obtained. The application for stock returns distribution are shown. The method of evaluating the tail probabilities is developed. The implementation of the Pearson type IV distribution could make a breakthrough for statistical modeling.