TABLE OF CONTENTS This chapter is dedicated to probability density estimation problems [60, 69, 75] Probability densities are useful for different purposes. For example, the efficiency of liquid-liquid extraction columns depends on the probability distributions of the drops. In image processing the probability density function of the brightness is commonly used [17]. Probability distributions are of greatest interest in the areas of probabilities and statistics. Among other things, they permit the calculation of the mathematical expectation of a given random variable. Many techniques exist for their estimation. We will present techniques based on the moments, series of rectangular pulses, polynomial representation and kernels, focusing our attention on three parametric approaches, namely, the expectation maximization (EM) [37, 61] and its extension based on the total kurtosis, the method based on neural networks [47], and finally an approach based on stochastic approximation techniques [77]. The emphasis here will be on numerical considerations pertinent to probability densities estimation. In fact, all the aforesaid shows the importance of these problems. Several simulations are presented in order to show the performance of these algorithms and to illustrate their implementation.
This chapter is organized as follows. The main probability distributions are given in the first part while the second part is dedicated to several estimation techniques which are illustrated by numerical simulations.
Probability distributions play an important role in many stochastic problems such as those related to systems reliability, image signal processing, etc. In this section we present the well-known probability density...
