On fitting cryptocurrency log-return exchange rates

Cryptocurrency has become the leading method for peer-to-peer electronic cash system. It uses cryptography to secure financial transactions. Recently, several researchers have attempted to understand the behaviors of cryptocurrency exchange rates. In this paper, we introduce a new location–scale family of distributions to understand the distributional properties of the log-return exchange rates of cryptocurrencies. We use quantile kurtosis measures to show that the proposed family of distributions provides a desirable level of flexibility in terms of skewness and tail heaviness. Several recent data on US dollar-based cryptocurrency exchange rates have been analyzed, and the results are compared against those of the generalized hypergeometric distribution. It is shown that the proposed family of distributions possesses desired features including model simplicity, shape flexibility and quality of distribution fit.