We elaborate on the tail conditional expectation, the tail conditional variance, and the tail variance when the residuals follow the standardized Pearson type-IV distribution. If the probability density function describing the data generation process is continuous and the moments are finite,...

The cumulative distribution function of the Pearson type IV distribution is of complex form and includes a complex hypergeometric function. Although the mathematical form is complex, the resulting imaginary part is actually of the order which is attributed to the series summation of the...

We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined via application of several statistical tests and risk...