**Sankhya: The Indian Journal of Statistics**

1995, Volume 57, Series A, Pt. 1, pp. 56--67

**KERNEL TYPE DENSITY ESTIMATES FOR POITIVE VALUED RANDOM VARIABLES**

By

ISHA BAGAI and B. L. S. PRAKASA RAO, *Indian Statistical Institute*

SUMMARY. We propose kernel type estimators for the density function of non negative random variables, where the kernel function is a probability density function on $(0, \infty)$. 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.

*AMS (1991) subject classification.* Primary 62G05; secondary 62N05.

*Key words and phrases.* Density estimation, Kernel-type estimators, reliability, standard exponential kernels.