An overview of generalized gamma Mittag-Leffler model and its applications (Q2422518)

Summary: Recently, probability models with thicker or thinner tails have gained more importance among statisticians and physicists because of their vast applications in random walks, Lévi flights, financial modeling, \textit{etc.} In this connection, we introduce here a new family of generalized probability distributions associated with the Mittag-Leffler function. This family gives an extension to the generalized gamma family, opens up a vast area of potential applications and establishes connections to the topics of fractional calculus, nonextensive statistical mechanics, Tsallis statistics, superstatistics, the Mittag-Leffler stochastic process, the Lévi process and time series. Apart from examining the properties, the matrix-variate analogue and the connection to fractional calculus are also explained. By using the pathway model of Mathai, the model is further generalized. Connections to Mittag-Leffler distributions and corresponding autoregressive processes are also discussed.