Non-uniform Estimates in the Approximation by the Irwin Law
Kazimieras Padvelskis
Vilnius Gediminas Technical University, Lithuania
Ruslan Prigodin
Vilnius Gediminas Technical University, Lithuania
Published 2016-12-20


cumulative distribution function
characteristic function
Irwin law
generalized Rademacher random variables
nonuniform estimates

How to Cite

Padvelskis K. and Prigodin R. (2016) “Non-uniform Estimates in the Approximation by the Irwin Law”, Lithuanian Journal of Statistics, 55(1), pp. 112-118. doi: 10.15388/LJS.2016.13873.


We consider an approximation of a cumulative distribution function F(x) by the cumulative distributionfunction G(x) of the Irwin law. In this case, a function F(x) can be cumulative distribution functions of sums (products) ofindependent (dependent) random variables. Remainder term of the approximation is estimated by the cumulant method.The cumulant method is used by introducing special cumulants, satisfying the V. Statulevičius type condition. The mainresult is a nonuniform bound for the difference |F(x)-G(x)| in terms of special cumulants of the symmetric cumulativedistribution function F(x).

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