Determination of the calculated level for the rain floods maximum flow

Abstract

It is proposed to use the Johnson distribution in determining the calculated level for rain floods. To determine the confidence intervals for estimating the Johnson distribution parameters obtained by the maximum likelihood method, authors propose the following sequence of actions: the construction of a system of equations for the maximum likelihood method; choice of the method of solving the system of equations for the maximum likelihood method; determination of the initial approximation of the system of equations for the maximum likelihood method; the solution of the system of equations for the maximum likelihood method; definition of elements for the information matrix; the determination of the limits of confidence intervals for the obtained parameter estimates. To solve the systems of equations for the maximum likelihood method, Newton's method is chosen. The expressions necessary to calculate the values of Jacobians entering the procedure for solving the resulting system are given. A method is given for obtaining an information matrix necessary for calculating the confidence intervals for estimates of the Johnson distribution parameters. Expressions for calculating the values of the Hessians involved in the procedure for calculating the variances of the obtained estimates for the Johnson distribution parameters are obtained. The technique for obtaining the calculated values of the rain floods maximum level is described.