1 research outputs found
On the symmetric and skew-symmetric K-distributions
We propose a family of four-parameter distributions that contain the
K-distribution as special case. The family is derived as a mixture distribution
that uses the three-parameter reflected Gamma distribution as parental and the
two-parameter Gamma distribution as prior. Properties of the proposed family
are investigated as well; these include probability density function,
cumulative distribution function, moments, and cumulants. The family is termed
symmetric K-distribution (SKD) based on its resemblance to the K-distribution
as well as its symmetric nature. The standard form of the SKD, which often
proves to be an adequate model, is also discussed. Moreover, an order
statistics analysis is provided as well as the distributions of the product and
ratio of two independent and identical SKD random variables are derived.
Finally, a generalisation of the proposed family, which enables non-zero
skewness values, is investigated, while both the SKD and the skew-SKD are
proven capable of describing the complex dynamics of machine learning, Bayesian
analysis and other fields through simplified expressions with high accuracy