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fixed co-ordinate to coordinate

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	~~Hello~~. ~~Allow me introduce the author~~. ~~Her title is Emilia Shroyer but it's not the most~~ [~~http:~~//~~hardinmd~~.~~lib~~.~~uiowa.edu~~/~~herpespictures.html feminine~~] ~~name out there~~. ~~Managing people~~ is ~~what I do and~~ the ~~wage~~ has been ~~really fulfilling~~. ~~California~~ is where ~~her house~~ is ~~but she needs to transfer simply because~~ of ~~her family members~~. ~~One~~ of the ~~extremely over~~ the ~~counter~~ [~~http~~:/~~/www~~.~~adosphere~~.~~com~~/~~member~~/~~28512~~/~~blog~~/~~view~~/~~66112~~/ ~~std home test~~] ~~test very best issues in~~ the ~~globe for me is to do aerobics and now I'm attempting to make cash with it.~~<br><br>~~Also visit my weblog at home [http:~~//~~chatmast~~.~~com~~/~~index~~.~~php?do~~=~~/BookerSipessk/info/ std testing at home~~] ~~testing~~ :: ~~[http:~~/~~/muzikoman~~.~~com/profile~~-~~682~~/~~info/ http~~:/~~/muzikoman~~.~~com/profile~~-~~682/info/~~]		{{Probability distribution\|
			name = Shifted Gompertz\|
			type =density\|
			pdf_image =[[File:Shiftedgompertz distribution PDF.svg\|325px\|Probability density plots of shifted Gompertz distributions]]\|
			cdf_image =[[File:Shiftedgompertz distribution CDF.svg\|325px\|Cumulative distribution plots of shifted Gompertz distributions]]\|
			parameters =<math>b>0</math> [[scale parameter\|scale]] ([[real number\|real]])<br/><math>\eta>0</math> [[shape parameter\|shape]] (real)\|
			support =<math>x \in [0, \infty)\!</math>\|
			pdf =<math>b e^{-bx} e^{-\eta e^{-bx}}\left[1 + \eta\left(1 - e^{-bx}\right)\right]</math>\|
			cdf =<math>\left(1 - e^{-bx}\right)e^{-\eta e^{-bx}}</math>\|
			mean =<math>(-1/b)\{\mathrm{E}[\ln(X)] - \ln(\eta)\}\,</math>
			where <math>X = \eta e^{-bx}\,</math> and
			<math>\begin{align}\mathrm{E}[\ln(X)] =& [1 {+} 1 / \eta]\!\!\int_0^\eta \!\!\!\! e^{-X}[\ln(X)]dX\\ &- 1/\eta\!\! \int_0^\eta \!\!\!\! X e^{-X}[\ln(X)] dX \end{align}</math>\|
			median =\|
			mode = <math>0 \text{ for }0 < \eta \leq 0.5</math><br/> <math>(-1/b)\ln(z^\star)\text{, for } \eta > 0.5</math><br/><math>\text{ where }z^\star = [3 + \eta - (\eta^2 + 2\eta + 5)^{1/2}]/(2\eta)</math>\|
			variance =<math>(1/b^2)(\mathrm{E}\{[\ln(X)]^2\} - (\mathrm{E}[\ln(X)])^2)\,</math>
			where <math>X = \eta e^{-bx}\,</math> and <math>\begin{align}\mathrm{E}\{[\ln(X)]^2\} =& [1 {+} 1 / \eta]\!\!\int_0^\eta \!\!\!\! e^{-X}[\ln(X)]^2 dX\\ &- 1/\eta \!\!\int_0^\eta \!\!\!\! X e^{-X}[\ln(X)]^2 dX \end{align}</math>\|
			skewness =\|
			kurtosis =\|
			entropy =\|
			mgf =\|
			char =\|
			}}
			The '''shifted Gompertz distribution''' is the distribution of the largest of two independent [[random variable]]s one of which has an [[exponential distribution]] with parameter b and the other has a [[Gumbel distribution]] with parameters <math>\eta</math> 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 ([[truncated distribution\|truncated]] at zero), the labelling can be considered as accurate. It has been used as a model of [[Diffusion of innovations\|adoption of innovations]]. It was proposed by Bemmaor (1994).

			== Specification ==

			===Probability density function===

			The [[probability density function]] of the shifted Gompertz distribution is:

			:<math> f(x;b,\eta) = b e^{-bx} e^{-\eta e^{-bx}}\left[1 + \eta\left(1 - e^{-bx}\right)\right] \text{ for }x \geq 0. \,</math>

			where <math>b > 0</math> is the [[scale parameter]] and <math>\eta > 0</math> is the [[shape parameter]] of the shifted Gompertz distribution.

			===Cumulative distribution function===

			The [[cumulative distribution function]] of the shifted Gompertz distribution is:

			:<math> F(x;b,\eta) = \left(1 - e^{-bx}\right)e^{-\eta e^{-bx}} \text{ for }x \geq 0. \,</math>

			== Properties ==
			The shifted Gompertz distribution is right-skewed for all values of <math>\eta</math>. It is more flexible than the [[Gumbel distribution]].

			===Shapes===
			The shifted Gompertz density function can take on different shapes depending on the values of the shape parameter <math>\eta</math>:
			* <math>0 < \eta \leq 0.5\,</math> the probability density function has its mode at 0.
			* <math>\eta > 0.5\,</math> the probability density function has its mode at
			::<math>\text{mode}=-\frac{\ln(z^\star)}{b}\, \qquad 0 < z^\star < 1</math>
			:where <math>z^\star\,</math> is the smallest root of
			::<math>\eta^2z^2 - \eta(3 + \eta)z + \eta + 1 = 0\,,</math>
			:which is
			::<math>z^\star = [3 + \eta - (\eta^2 + 2\eta + 5)^{1/2}]/(2\eta).</math>

			== Related distributions ==
			If <math>\eta</math> varies according to a [[gamma distribution]] with shape parameter <math>\alpha</math> and scale parameter <math>\beta</math> (mean = <math>\alpha\beta</math>), the distribution of <math>x</math> is Gamma/Shifted Gompertz (G/SG). When <math>\alpha</math> is equal to one, the G/SG reduces to the [[Bass model]].

			== See also ==
			*[[Gumbel distribution]]
			*[[Generalized extreme value distribution]]
			*[[Mixture model]]
			*[[Bass model]]
			*[[Gompertz distribution]]

			== References ==
			{{No footnotes\|date=April 2012}}
			*{{Cite book \| last=Bemmaor \| given=Albert C. \| year= 1994 \|pages=201–223\| chapter=Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity \| editor=G. Laurent, G.L. Lilien & B. Pras \| title=Research Traditions in Marketing \| publisher=Kluwer Academic Publishers \| place=Boston\| ISBN=0-7923-9388-0}}
			*{{Cite book\| last1=Chandrasekaran\| given1=Deepa \| surname2=Tellis\| given2=Gerard J. \|year= 2007 \|volume=3\| chapter=A Critical Review of Marketing Research on Diffusion of New Products \| editor=Naresh K. Malhotra \| title=Review of Marketing Research \| publisher=M.E. Sharpe \| place=Armonk \| pages = 39–80 \| ISBN = 978-0-7656-1306-6}}
			*{{Cite journal
			\| last1 = Dover
			\| first1 = Yaniv
			\| title = Network Traces on Penetration: Uncovering Degree Distribution From Adoption Data
			\| first2 = Jacob \|last2=Goldenberg
			\| first3 = Daniel \|last3=Shapira
			\| journal = Marketing Science\|doi=10.1287/mksc.1120.0711 \|year=2012 }}
			*{{Cite journal
			\| last1 = Jimenez
			\| first1 = Fernando
			\| title = A Note on the Moments and Computer Generation of the Shifted Gompertz Distribution
			\| first2 = Pedro \|last2=Jodra
			\| journal = Communications in Statistics - Theory and Methods
			\| volume = 38 \| issue = 1
			\| pages = 78–89
			\| year = 2009
			\| doi=10.1080/03610920802155502}}
			*{{Cite journal
			\| last1 = Van den Bulte
			\| first1 = Christophe
			\| title = Social Contagion and Income Heterogeneity in New Product Diffusion: A Meta-Analytic Test
			\| first2 = Stefan \|last2=Stremersch
			\| journal = Marketing Science
			\| volume = 23 \| issue = 4
			\| pages = 530–544
			\| year = 2004
			\| doi = 10.1287/mksc.1040.0054}}

			{{ProbDistributions\|continuous-semi-infinite}}

			[[Category:Continuous distributions]]
			[[Category:Probability distributions]]

189.107.58.218 at 17:31, 20 June 2012

2012-06-20T17:31:49Z

New page

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Perpendicular axis theorem - Revision history

en>Assosiation: fixed co-ordinate to coordinate

en>ClueBot NG: Reverting possible vandalism by 119.152.30.180 to version by Addbot. False positive? Report it. Thanks, ClueBot NG. (1631840) (Bot)

189.107.58.218 at 17:31, 20 June 2012