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关注这篇论文的作者
Irving W. Burr
Peter J. Cislak

原文摘要

This paper presents the region of coverage of the curve shape characteristics, α23 and δ = (2α4 −3α23 −6) /(α4+3), for a certain general system of distributions, Burr (1942). These curve-shape characteristics were chosen for comparison with the Pearson system because of the simplicity with which they map the members of the latter system, Craig (1936). It is here shown that the present system covers almost all of the regions of the main Pearson Types IV and VI, and an important part of that of the main Type I (or beta distribution). The density function of the median for odd sized samples from the present system is given in closed form. All finite moments of the median are linear combinations of beta functions. Important characteristics of the median: bias, and efficiency relative to the sample mean, are given for samples of n = 3, 5, 7 and 11, for populations with α3:x = 0, .50, 1.00, 1.50, and, corresponding to each α3:x two well separated α4:x, values. It also appears that for this system, the median begins to be more efficient than the mean at about the degree of non-normality of the exponential distribution.

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