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Indeed, we know that if X is an exponential r.v. with rate λ, then cX is an exponential r.v. with rate λ/c; the same thing is valid with Gamma variates (and this can be checked using the moment-generating function, see, e.g.,these notes, 10.4-(ii)): multiplication by a positive constant c divides the rate (or, equivalently, multiplies the scale).
The probability density function of Gamma distribution for different parameters. See below for the spec and Gnuplot source code. Date: 26 June 2010, 18:31 (UTC) Source: Gamma_distribution_pdf.png; Author: Gamma_distribution_pdf.png: MarkSweep and Cburnett; derivative work: Autopilot (talk)
Thus computing the gamma function becomes a matter of evaluating only a small number of elementary functions and multiplying by stored constants. The Lanczos approximation was popularized by Numerical Recipes , according to which computing the gamma function becomes "not much more difficult than other built-in functions that we take for granted ...
as the only positive function f , with domain on the interval x > 0, that simultaneously has the following three properties: f (1) = 1, and f (x + 1) = x f (x) for x > 0 and f is logarithmically convex. A treatment of this theorem is in Artin's book The Gamma Function, [4] which has been reprinted by the AMS in a collection of Artin's writings.
The quantile function can be found by noting that (;,,) = ((/)) where is the cumulative distribution function of the gamma distribution with parameters = / and =. The quantile function is then given by inverting F {\displaystyle F} using known relations about inverse of composite functions , yielding:
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
Intensity modulated radiation therapy (IMRT) is an advanced radiotherapy technique used to minimize the amount of normal tissue being irradiated in the treatment field. In some systems, this intensity modulation is achieved by moving the leaves in the MLC during the course of treatment, thereby delivering a radiation field with a non-uniform (i ...
Academic Torrents [1] [2] [3] [4] [5] [6] is a website which enables the sharing of research data using the BitTorrent protocol. The site was founded in November 2013 ...