Kernel type density estimates for positive valued random variables

Abstract

We propose kernel type estimators for the density function of non negative random variables, where the kernel function is a probability density function on (0, ∞). Properties of these estimators are discussed. A kernel, that minimizes the integrated mean square error is obtained. It is shown, however, that any reasonable kernel gives almost the same mean square error. On the basis of simulation studies the use of exponential kernels is recommended.