Negative binomial sum of random variables and modeling financial data

Abstract

A limiting probability distribution of negative binomial sum of independently and identically distributed random variable is obtained, which we call Negative Binomial Stable (NBS) distribution. It is applied in the forecasting of market changes by fitting the pound exchange rate change in relation with the Indian rupees. Using the data we empirically compare normal, stable, geometric stable (GS) and NBS distributions. Among which the NBS distribution shows better fit than the normal, stable and GS models judged in terms of Kolmogrov distance test. The NBS model is a generalization of the GS model.