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Power-law confusion: You say incremental, I say differentialPower-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.
Document ID
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Colwell, Joshua E.
(Colorado Univ. Boulder, CO, United States)
Date Acquired
September 6, 2013
Publication Date
January 1, 1993
Publication Information
Publication: Lunar and Planetary Inst., Twenty-fourth Lunar and Planetary Science Conference. Part 1: A-F
Subject Category
Statistics And Probability
Accession Number
Distribution Limits
Work of the US Gov. Public Use Permitted.

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