کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1148583 | 957841 | 2007 | 22 صفحه PDF | دانلود رایگان |
We find the distribution that has maximum entropy conditional on having specified values of its first r LL-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.
Journal: Journal of Statistical Planning and Inference - Volume 137, Issue 9, 1 September 2007, Pages 2870–2891