Problems in Calculating Moments and Distribution Functions of Ladder Heights

详细

The problem of approximate calculation of distribution functions of ladder heights is considered in the context of the finite number of its known moments. This problem is solved by means of the Chebyshev continued fractions method. The midpoint is finding the terms of fraction of the nth convergents of continued fractions. The moments are calculated by S. Nagaev’s formulas, including solution of the Frobenius equation and applying the Fa di Bruno formulas for higher derivatives. The problem of high precision calculations is studied.