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Shifted Gompertz distribution : ウィキペディア英語版
Shifted Gompertz distribution
\left(+ \eta\left(1 - e^\right)\right )|
cdf =\left(1 - e^\right)e^() - \ln(\eta)\}\,
where X = \eta e^\, and
\begin\mathrm() =& ( 1 / \eta )\!\!\int_0^\eta \!\!\!\! e^()dX\\ &- 1/\eta\!\! \int_0^\eta \!\!\!\! X e^() dX \end|
median =|
mode = 0 \text0 < \eta \leq 0.5
(-1/b)\ln(z^\star)\text \eta > 0.5
\textz^\star = (+ \eta - (\eta^2 + 2\eta + 5)^ )/(2\eta)|
variance =(1/b^2)(\mathrm\ - (\mathrm())^2)\,
where X = \eta e^\, and \begin\mathrm\ =& ( 1 / \eta )\!\!\int_0^\eta \!\!\!\! e^()^2 dX\\ &- 1/\eta \!\!\int_0^\eta \!\!\!\! X e^()^2 dX \end|
skewness =|
kurtosis =|
entropy =|
mgf =|
char =|
}}
The shifted Gompertz distribution is the distribution of the largest of two independent random variables one of which has an exponential distribution with parameter b and the other has a Gumbel distribution with parameters \eta and b. In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution, the labelling can be considered as accurate. It has been used as a model of adoption of innovations. It was proposed by Bemmaor (1994). Some of its statistical properties have been studied further by Jiménez and Jodrá (2009).
It has been used to predict the growth and decline of social networks and on-line services and shown to be superior to the Bass model and Weibull distribution (see the work by Christian Bauckhage and co-authors).
== Specification ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Shifted Gompertz distribution」の詳細全文を読む



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