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.

翻译：我们作为特例提出一个四参数分布式家庭,其中含有K分布式。家庭作为混合分布式分配式,使用三参数反映Gamma分布式作为亲父母,用两参数分配式分配式作为双参数。还调查了拟议家庭的属性;其中包括概率密度功能、累积分布式功能、瞬间和蓄积体。家庭根据其与K分布式的相似性及其对称性质被称为对称K分布式分配式(SKD)。还讨论了SKD的标准形式,该标准形式往往证明是一个适当的模型。此外,还提供了订单统计分析,以及产品分布和两个独立和相同的SKD随机变量的比率。最后,对拟议家庭进行了概括性调查,使非零微宽度值成为可能,而SKD和Skew-SKD已证明能够通过高度准确的简化表达方式描述机器学习、Bayesian分析和其他领域的复杂动态。