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Two-Dimensional Distribution Law of Random Variables Having S. N. Kritskii and M. F. Menkel Three-Parameter Gamma Distributions: A Symmetrical Case

  • WATER RESOURCES AND THE REGIME OF WATER BODIES
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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.

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REFERENCES

  1. Bolgov, M.V., Sarmanov, I.O., and Sarmanov, O.V., Markovskie protsessy v gidrologii (Markov Processes in Hydrology), Moscow: Inst. Vodn. Probl. Ross. Akad. Nauk, 2009.

  2. Pugachev, V.S., Teoriya sluchainykh funktsii i ee primenenie k zadacham avtomaticheskogo upravleniya (Theory of Random Functions and Its Application to Automated Control Problems), Moscow: Fizmatlit, 1962.

  3. Pul’siruyushchee ozero Chany (Pulsating Chany Lake), Leningrad: Nauka, 1982.

  4. Ratkovich, D.Ya., Stochastic model of variations of the annual river runoff, Vodn. Resur., 1972, no. 1, pp. 52–94.

  5. Szego, G., Orthogonal Polynomials, Amer. Math. Soc., 1959.

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Funding

The study was carried out under Governmental Order to WPI RAS, subject no. 0147-2019-0003, state registration no. AAAA-A18-118022090105-5).

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Authors and Affiliations

  1. Water Problems Institute, Russian Academy of Sciences, 119333, Moscow, Russia

    M. V. Bolgov & I. O. Sarmanov

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  1. M. V. Bolgov
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  2. I. O. Sarmanov
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Correspondence to M. V. Bolgov.

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Translated by G. Krichevets

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Bolgov, M.V., Sarmanov, I.O. Two-Dimensional Distribution Law of Random Variables Having S. N. Kritskii and M. F. Menkel Three-Parameter Gamma Distributions: A Symmetrical Case. Water Resour 47, 517–520 (2020). https://doi.org/10.1134/S009780782004003X

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  • DOI: https://doi.org/10.1134/S009780782004003X

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