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Keywords:
distribution function; kernelapproximation; non-negative random variable
distribution function; kernelapproximation; non-negative random variable
Summary:
The problem of estimation of distribution functions or fractiles of non- negative random variables often occurs in the tasks of risk evaluation. There are many parametric models, however sometimes we need to know also some information about the shape and the type of the distribution. Unfortunately, classical approaches based on kernel approximations with a symmetric kernel do not give any guarantee of non-negativity for the low number of observations. In this note a heuristic approach, based on the assumption that non-negative distributions can be also approximated by means of kernels which are defined only on the positive real numbers, is discussed.
References:
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[2] Devroye L., Györfi L.: Nonparametric Density Estimation the $L_1$-view. Wiley, New York 1985 MR 0780746
[3] Albrecher H.: Dependent Risks and Ruin Probabilities in Insurance. Interim Report, IIASA, IR 98 072
[4] Rao C. R.: Linear Statistical Inference and its Applications (Czech translation). Academia, Praha 1978
[5] Rényi A.: Theory of Probability (Czech translation). Academia, Praha 1972 MR 0350789
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