Abstract #300816

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JSM 2002 Abstract #300816
Activity Number: 67
Type: Topic Contributed
Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical & Engineering Sciences*
Abstract - #300816
Title: Maximum Entropy, L-Moments, and Order Statistics
Author(s): Jonathan Hosking*+
Affiliation(s): IBM Research Division
Address: P.O. Box 218, Yorktown Heights, New York, 10598, U.S.A.
Keywords: density quantile function ; order statistics ; entropy ; L-moments, ; logistic distribution
Abstract:

We find the distribution that has maximum entropy conditional on having specified values of its first r L-moments. This condition is equivalent to specifying the expected values of the order statistics of a sample of size r. We show that 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 that may be useful for modeling data.

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