TABLE OF CONTENTS Sometimes, the properties of the physical stochastic process under analysis suggest the form of the underlying probability distribution. For example, if a process is composed of the sum of many individual effects, the gaussian distribution may be appropriate on the basis of the central limit theorem. Nevertheless, there are occasions when the required probability distribution has to be determined empirically, that is based solely on the available data.
In practice, the functional form of the probability distribution underpinning a given process is often not easy to derive. Furthermore, an assumed probability distribution (developed theoretically or determined empirically) may be confirmed, or disapproved, in the light of available data using certain statistical tests, known as 'goodness-of-fit' tests.
The simplest and longest used method for parameter estimation is that of probability plotting. This methodology involves plotting the failure times on a specifically-constructed plotting paper to determine the fit of the data to a given distribution and, if applicable, estimates of the distribution parameters.
Graph papers for plotting observed experimental data and their corresponding cumulative frequencies are called 'probability papers'. Probability papers are constructed such that a given probability paper is associated with a specific probability distribution.
Preferably, a probability paper should be constructed using a transformed probability scale in such a manner as to obtain a linear graph between the cumulative probabilities of the underlying distribution and the corresponding values of the variate. Then, the linearity, or lack of linearity, of a set...
