Model to Increase the Number of Output States of a Random Variable Using a Histogram Based PDF

This paper is devoted to a pseudo-random number generator that generates numbers according to a known probability density function. This function has its origins in a histogram that contains the observed properties of a monitored random variable X. Using the recorded PDF and an ON/OFF model we are able to generate output states of a random variable Y, which is nearly alike distributed as the random variable X. Because the used PDF has its origins in a normed histogram function, the resulting number of all possible output states of variable Y is the same as the number of classes that are used to form the histogram. We propose this model that generates practically an unlimited set of possible output states of the random variable Y. At first a cumulative distribution function is formed from the input density function. Then the ON/OFF model driven by a random number generator in (0, 1) is applied to address classes that are defined in the distribution function. To address these classes a search function is applied. Then when a class is chosen, we propose to use a second uniform random number generator that generates numbers within the range of the selected class. The resulting output state of the variable Y is the output of the second random number generator. In this paper we apply this model on a packet generator that generates IPTV inter-departure times of an MPEG2-TS H.264 VBR based video source.