  The probability distribution of precipitation amount strongly depends on
geography, climate zone, and time scale considered. Closed-form parametric
probability distributions are not sufficiently flexible to provide accurate and
universal models for precipitation amount over different time scales. In this
paper we derive non-parametric estimates of the cumulative distribution
function (CDF) of precipitation amount for wet periods. The CDF estimates are
obtained by integrating the kernel density estimator leading to semi-explicit
CDF expressions for different kernel functions. We investigate an adaptive
plug-in bandwidth (KCDE), using both synthetic data sets and reanalysis
precipitation data from the Mediterranean island of Crete (Greece). We show
that KCDE provides better estimates of the probability distribution than the
standard empirical (staircase) estimate and kernel-based estimates that use the
normal reference bandwidth. We also demonstrate that KCDE enables the
simulation of non-parametric precipitation amount distributions by means of the
inverse transform sampling method.
