Entry
Math:Probability:Distribution:Gamma:Can you describe Gamma distribution C^k.e^(-C.T).T^(k-1)/(k-1)!?
Dec 28th, 2004 09:23
Knud van Eeden,
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--- Knud van Eeden --- 28 December 2004 - 05:50 pm -------------------
Math:Probability:Distribution:Gamma:Can you describe Gamma
distribution C^k.e^(-C.T).T^(k-1)/(k-1)!?
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Definition of the Gamma probability function.
k -(C.T) (k-1)
= C . e . T (1)
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Gamma( k )
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The gamma distribution is a special case of a continuous probability
distribution.
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The gamma distribution is a general type of statistical distribution
(occurring e.g. in processes in which you want to know the
waiting time intervals between events described by Poisson
distributions, like the waiting time between telephone calls)
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You can derive it by differentiating its cumulative probability
function, which is a sum of Poisson distributions.
See e.g. the Erlang distribution description for a derivation,
otherwise [Eric Weisstein]
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History:
Appeared first in statistics in the 1930s
(used by Karl Pearson and later Charles Ernest Weatherburn)
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Note:
'Gamma family' of distributions:
The exponential distribution, Poisson distribution and Gamma
distribution are sometimes called the 'Gamma family',
so clearly indicating, emphasizing and associating that it is a group,
collection belonging together.
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Book: see also:
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[book: Drake, Alvin W. - Fundamentals of Applied Probability Theory -
Mcgraw-Hill - http://www.amazon.com/exec/obidos/tg/detail/-
/0070178151/qid=1104254766/sr=8-1/ref=sr_8_xs_ap_i1_xgl14/104-5080812-
8575144?v=glance&s=books&n=507846]
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[book: Hastings, Kevin J. - Probability and statistics - ISBN 0-201-
59278-9 - p. 133-140 'Gamma density' (good description, also
explaining briefly the link between a Poisson process interval and the
exponential function). Calls the exponential distribution, Poisson
distribution and Gamma distribution the 'Gamma family')]
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[book: Ross, Sheldon M. - Introduction to Probability Models -
http://www.amazon.com/exec/obidos/ASIN/0125980558/qid=1104254849/sr=2-
1/ref=pd_ka_b_2_1/104-5080812-8575144]
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[book: Spanier, Jerome / Oldham, Keith B. - an atlas of functions -
ISBN 0-89116-573-8 - p. 260 'Gamma distribution' (only some formulas
with a short description)]
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[book: Weisstein, Eric - CRC encyclopedia mathematics - p. 694 'Gamma
distribution' (a good description, lots of formulas and a few graphs)]
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[book: Zwillinger, Daniel - CRC standard mathematical tables and
formula - p. 584 'Gamma distribution' (only some formulas with a short
description)]
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Internet: see also:
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Gamma distribution: history
http://members.aol.com/jeff570/g.html
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Charles Ernest Weatherburn
http://www-groups.dcs.st-
and.ac.uk/~history/Mathematicians/Weatherburn.html
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Karl Pearson
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pearson.html
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Gamma distribution (showing graphs)
http://en.wikipedia.org/wiki/Gamma_distribution
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Gamma distribution (Showing a graph / see (5) 'The corresponding
probability function P(x) of waiting times until the hth Poisson event
is then obtained by differentiating D(x)')
http://mathworld.wolfram.com/GammaDistribution.html
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Math: Probability: Distribution: Link: Overview: Can you give an
overview of links?
http://www.faqts.com/knowledge_base/view.phtml/aid/32917/fid/815
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