Numeric Representation of Probability Density Functions

In my thesis, I explore the concept of the Numeric Density Function, first introduced by W. Kleinöder. This representation uses numeric values to model probability density functions, offering an efficient way to perform operations like the convolution of distributions. Essentially, the function condenses a probability density into a finite number of values, each calculated using integrals of equal width. By adjusting the width, one can control the precision of the stored values. These functions play a crucial role in tools like PEPP.

PEPP (Performance Evaluation of Parallel Programs), developed by Franz Hartleb and his team, estimates the execution time of parallel programs using a stochastic graph model. In this model, each task is represented as a node, and random variables, associated with probability density functions (and their NDF representation), are used to simulate execution times.

For my thesis, a working implementation of the NDF approach was developed, featuring a user interface created in Java. This tool can generate NDFs for exponential and Erlang distributions while maintaining accuracy within a certain error margin. Along with binary operators like convolution, minimum, and maximum, the tool can simulate phase-type distributions via the Cox representation. The thesis outlines the mathematical principles behind NDFs, details the implementation, and describes the user interface and its features.