We introduce two extensions of the canonical Feller–Spitzer distribution from the class of Bessel densities, which comprise two distinct stochastically decreasing one-parameter families of positive absolutely continuous infinitely divisible distributions with monotone densities, whose upper tails exhibit a power decay. The densities of the members of the first class are expressed in terms of the modified Bessel function of the first kind, whereas the members of the second class have the densities of their Lévy measure given by virtue of the same function. The Laplace transforms for both these families possess closed–form representations in terms of specific hypergeometric functions. We obtain the explicit expressions by virtue of the particular parameter value for the moments of the distributions considered and establish the monotonicity of the mean, variance, skewness and excess kurtosis within the families. We derive numerous properties of members of these classes by employing both new and previously known properties of the special functions involved and determine the variance function for the natural exponential family generated by a member of the second class.
|Number of pages||25|
|Journal||Journal of Statistical Distributions and Applications|
|Early online date||4 Mar 2021|
|Publication status||Published - 4 Mar 2021|
|Event||3rd International Conference on Statistical Distributions and Applications - Eberhard Conference Center, Grand Rapids, United States|
Duration: 10 Oct 2019 → 12 Oct 2019
Conference number: 3rd