Parameter-free testing of the shape of a probability distribution

The Kolmogorov–Smirnov test determines the consistency of empirical data with a particular probability distribution. Often, parameters in the distribution are unknown, and have to be estimated from the data. In this case, the Kolmogorov–Smirnov test depends on the form of the particular probability distribution under consideration, even when the estimated parameter-values are used within the distribution. In the present work, we address a less specific problem: to determine the consistency of data with a given functional form of a probability distribution (for example the normal distribution), without enquiring into values of unknown parameters in the distribution. For a wide class of distributions, we present a direct method for determining whether empirical data are consistent with a given functional form of the probability distribution. This utilizes a transformation of the data. If the data are from the class of distributions considered here, the transformation leads to an em...

• Type: Journal
• Year: 2007
• Where: BIOSYSTEMS
• Authors: M. Broom, P. Nouvellet, J. P. Bacon, D. Waxman
• Keywords: BIOSYSTEMS 2007, Kolmogorov–Smirnov Test, Particular Probability Distribution, Probability Distribution