Abstract

A method for constructing two-dimensional distribution law in a symmetrical case for three-parameter Kritskii and Menkel distribution is considered, and some results of the application of the model in applied hydrological studies are discussed. A system of orthogonal functions with a weight function in the form of a three-parameter gamma distribution is proposed to obtain linear correlation between three-parameter variables. Orthogonalization method was used to obtain an expression for symmetric two-dimensional density satisfying Markov equation and having a linear regression equation. The results of stochastic simulation of water level variations in the drainless Chany Lake, carried out with the use of the proposed model, showed that the use of linear correlation leads to a value of asymmetry of the level distribution that is in a good agreement with sample estimates of these parameter based on observation data.

中文翻译：

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具有SN Kritskii和MF Menkel三参数Gamma分布的随机变量的二维分布定律：一个对称情况

摘要

考虑了一种在三参数Kritskii和Menkel分布的对称情况下构造二维分布规律的方法，并讨论了该模型在应用水文研究中的一些应用结果。为了获得三参数变量之间的线性相关性，提出了一种具有三参数伽马分布形式的权函数的正交函数系统。使用正交化方法获得满足Markov方程并具有线性回归方程的对称二维密度表达式。利用所提出的模型进行了无排水沟的钱尼湖水位变化的随机模拟结果，