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Determination of confidence intervals of Kritsky-Menckel distribution parameters

V. Dubnitskiy, O. Petrenko, A. Khodyrev
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Description: For determining of the confidence intervals of the Kritsky-Menckel distribution parameters estimates which obtained by the maximum likelihood method, a sequence of actions is proposed. The sequence consists of the following stages: construction of the equations system for the maximum likelihood method; choice of the method for solving the system of equations of the maximum likelihood method; determination of the initial approximation for the system of equations of the maximum likelihood method; the solution of the system of equations of the maximum likelihood method; the definition of elements of the Fisher information matrix; the determination of the confidence intervals boundaries for the obtained estimates of the Kritsky-Menckel distribution parameters. To solve the systems of equations of the maximum likelihood method, Newton's method was chosen. The initial approximation was obtained by the technique of using the graphoanalytical method. The necessary expressions for calculating the values of Jacobeans that entered the procedure of solving the resulting system are given. The method for obtaining the Fisher information matrix is given. This method is necessary for calculating the confidence intervals for estimates of the Kritsky-Menckel distribution parameters. The expressions necessary for calculating the values of the Hessians involved in the procedure for calculating the variances of the obtained estimates of the Kritsky-Menckel distribution parameters are obtained. The expressions for the determination of confidence intervals for the distribution of Kritsky-Menckel are given.


Keywords: Kritsky-Menckel distribution, maximum likelihood method, estimates of the Kritsky-Menckel distribution, confidence intervals for the estimates of the Kricki-Menckel distribution

Reference:
Dubnitskii, V.Iu., Petrenko, O.E. and Khodyrev, A.I. (2018), “Opredelenie doveritelnykh intervalov parametrov raspredeleniia Kritskogo-Menkelia” [Determination of confidence intervals of Kritsky-Menckel distribution parameters], Information Processing Systems, Vol. 2(153), pp. 81-87. https://doi.org/10.30748/soi.2018.153.10.