Template:Gamma distribution: Difference between revisions

Latest revision as of 08:50, 3 August 2012

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-{{gamma distribuiton introduction}}
+#REDIRECT [[The_Gamma_Distribution]]
-{{gamma probability density function}}
-{{gamma reliability function}}
-{{gamma mean median and mode}}
-{{gamma standard deviation}}
-{{gamma reliable life}}
-{{gamma failure rate function}}
-{{characteristics of the gamma distribution}}
-{{gd confidence bounds}}
-===Bounds on Time===
-The bounds around time for a given gamma percentile (unreliability) are estimated by first solving the reliability equation with respect to time, as follows:
-::<math>\widehat{T}(\widehat{\mu },\widehat{\sigma })=\widehat{\mu }+\widehat{\sigma }z</math>
-:where:
-::<math>z=\ln (-\ln (R))</math>
-::<math>Var(\widehat{T})={{(\frac{\partial T}{\partial \mu })}^{2}}Var(\widehat{\mu })+2(\frac{\partial T}{\partial \mu })(\frac{\partial T}{\partial \sigma })Cov(\widehat{\mu },\widehat{\sigma })+{{(\frac{\partial T}{\partial \sigma })}^{2}}Var(\widehat{\sigma })</math>
-:or:
-::<math>Var(\widehat{T})=Var(\widehat{\mu })+2\widehat{z}Cov(\widehat{\mu },\widehat{\sigma })+{{\widehat{z}}^{2}}Var(\widehat{\sigma })</math>
-The upper and lower bounds are then found by:
-::<math>\begin{align}
-  & {{T}_{U}}= & \hat{T}+{{K}_{\alpha }}\sqrt{Var(\hat{T})}\text{ (Upper bound)} \\
- & {{T}_{L}}= & \hat{T}-{{K}_{\alpha }}\sqrt{Var(\hat{T})}\text{ (Lower bound)}
-\end{align}</math>
-{{gamma distribution example}}