Template:Generalized gamma reliability function - Revision history

Lisa Hacker: Redirected page to The Generalized Gamma Distribution

2012-08-09T09:36:49Z

Redirected page to The Generalized Gamma Distribution

← Older revision		Revision as of 09:36, 9 August 2012
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	~~===Generalized Gamma Reliability Function===~~		#REDIRECT [[The_Generalized_Gamma_Distribution]]
	~~The reliability function for the generalized gamma distribution is given by:~~

	~~::<math>R(t)=\left\{ \begin{array}{*{35}{l}}~~
	~~1-{{\Gamma }_{I}}\left( \tfrac{{{e}^{\lambda \left( \tfrac{\text{ln}(t)-\mu }{\sigma } \right)}}}{{{\lambda }^{2}}};\tfrac{1}{{{\lambda }^{2}}} \right)\text{ if }\lambda >0 \\~~
	~~1-\Phi \left( \tfrac{\text{ln}(t)-\mu }{\sigma } \right)\text{ if }\lambda =0 \\~~
	~~{{\Gamma }_{I}}\left( \tfrac{{{e}^{\lambda \left( \tfrac{\text{ln}(t)-\mu }{\sigma } \right)}}}{{{\lambda }^{2}}};\tfrac{1}{{{\lambda }^{2}}} \right)\text{ if }\lambda <0 \\~~
	~~\end{array} \right.</math>~~

	~~where:~~

	~~::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z}{{e}^{-\tfrac{{{x}^{2}}}{2}}}dx</math>~~

	~~and <math>{{\Gamma }_{I}}(k;x)</math> is the incomplete gamma function of <math>k</math>~~

	~~and <math>x</math> , which is given by:~~

	~~::<math>{{\Gamma }_{I}}(k;x)=\frac{1}{\Gamma (k)}\int_{0}^{x}{{s}^{k-1}}{{e}^{-s}}ds</math>~~

	~~where <math>\Gamma (x)</math> is the gamma function of <math>x</math> .~~
	~~Note that in Weibull++ the probability plot of the generalized gamma is created on lognormal probability paper. This means that the fitted line will not be straight unless <math>\lambda =0.</math>~~

Harry Guo: /* Generalized Gamma Reliability Function */

2012-02-14T21:05:00Z

Generalized Gamma Reliability Function

← Older revision		Revision as of 21:05, 14 February 2012
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	\end{array} \right.</math>		\end{array} \right.</math>

	:where:		where:

	::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z}{{e}^{-\tfrac{{{x}^{2}}}{2}}}dx</math>		::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z}{{e}^{-\tfrac{{{x}^{2}}}{2}}}dx</math>

Nicolette Young: Created page with '===Generalized Gamma Reliability Function=== The reliability function for the generalized gamma distribution is given by: :: $R(t)=\left\{ \begin{array}{*{35}{l}} 1-{{\Ga…'$

2012-01-04T21:08:56Z

Created page with '===Generalized Gamma Reliability Function=== The reliability function for the generalized gamma distribution is given by: ::<math>R(t)=\left\{ \begin{array}{*{35}{l}} 1-{{\Ga…'

New page

===Generalized Gamma Reliability Function===
The reliability function for the generalized gamma distribution is given by:

::<math>R(t)=\left\{ \begin{array}{*{35}{l}}
1-{{\Gamma }_{I}}\left( \tfrac{{{e}^{\lambda \left( \tfrac{\text{ln}(t)-\mu }{\sigma } \right)}}}{{{\lambda }^{2}}};\tfrac{1}{{{\lambda }^{2}}} \right)\text{ if }\lambda >0 \\
1-\Phi \left( \tfrac{\text{ln}(t)-\mu }{\sigma } \right)\text{ if }\lambda =0 \\
{{\Gamma }_{I}}\left( \tfrac{{{e}^{\lambda \left( \tfrac{\text{ln}(t)-\mu }{\sigma } \right)}}}{{{\lambda }^{2}}};\tfrac{1}{{{\lambda }^{2}}} \right)\text{ if }\lambda <0 \\
\end{array} \right.</math>

:where:

::<math>\Phi (z)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{z}{{e}^{-\tfrac{{{x}^{2}}}{2}}}dx</math>

and <math>{{\Gamma }_{I}}(k;x)</math> is the incomplete gamma function of <math>k</math>

and <math>x</math> , which is given by:

::<math>{{\Gamma }_{I}}(k;x)=\frac{1}{\Gamma (k)}\int_{0}^{x}{{s}^{k-1}}{{e}^{-s}}ds</math>

where <math>\Gamma (x)</math> is the gamma function of <math>x</math> .
Note that in Weibull++ the probability plot of the generalized gamma is created on lognormal probability paper. This means that the fitted line will not be straight unless <math>\lambda =0.</math>

Template:Generalized gamma reliability function - Revision history

Lisa Hacker: Redirected page to The Generalized Gamma Distribution

Harry Guo: /* Generalized Gamma Reliability Function */

Nicolette Young: Created page with '===Generalized Gamma Reliability Function=== The reliability function for the generalized gamma distribution is given by: ::R(t)=\left\{ \begin{array}{*{35}{l}} 1-{{\Ga…'

Nicolette Young: Created page with '===Generalized Gamma Reliability Function=== The reliability function for the generalized gamma distribution is given by: :: $R(t)=\left\{ \begin{array}{*{35}{l}} 1-{{\Ga…'$