Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
We find the distribution that has maximum entropy conditional on having specified values of its first rL -moments. This condition is equivalent to specifying the expected values of the order statistics of a sample of size r. The maximum-entropy distribution has a density-quantile function, the reciprocal of the derivative of the quantile function, that is a polynomial of degree r; the quantile function of the distribution can then be found by integration. This class of maximum-entropy distributions includes the uniform, exponential and logistic, and two new generalizations of the logistic distribution. It provides a new method of nonparametric fitting of a distribution to a data sample. We also derive maximum-entropy distributions subject to constraints on expected values of linear combinations of order statistics. © 2007 Elsevier B.V. All rights reserved.
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
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