Abstract
A new heavy-tailed distribution is considered in this paper: the p-generalized Cauchy distribution. This new 5-parameter distribution family is substantially more flexible than than the classical Cauchy distribution, it contains, in particular, asymmetric distributions. Various numerical characteristics of the new distribution are considered, among them are fractional order moments and “twice incomplete” moments. There were obtained also (using numerical methods) values of quantile-based standardized moments of higher orders: Bowley’s skewness and Moors’ kurtosis. Suitability of the p-generalized Cauchy distribution for modeling real data was confirmed by fitting this distribution to a series of log returns of stock prices. The p-generalized Cauchy distribution had the smaller value of the AIC statistic than the Cauchy distribution, the skew Cauchy distribution, the generalized logistic distribution and the hyperbolic distribution.
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