Template:Fisher Matrix Confidence Bounds ED: Difference between revisions

Latest revision as of 06:55, 10 August 2012

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-===Fisher Matrix Bounds===
+#REDIRECT [[The Exponential Distribution]]
-{{Bounds on the Parameters FMB ED}}
-====Bounds on Reliability====
-The reliability of the two-parameter exponential distribution is:
-::<math>\hat{R}(T;\hat{\lambda })={{e}^{-\hat{\lambda }(T-\hat{\gamma })}}</math>
-The corresponding confidence bounds are estimated from:
-::<math>\begin{align}
-  & {{R}_{L}}= & {{e}^{-{{\lambda }_{U}}(T-\hat{\gamma })}} \\
- & {{R}_{U}}= & {{e}^{-{{\lambda }_{L}}(T-\hat{\gamma })}}
-\end{align}</math>
-These equations hold true for the one-parameter exponential distribution, with <math>\gamma =0</math>.
-====Bounds on Time====
-The bounds around time for a given exponential percentile, or reliability value, are estimated by first solving the reliability equation with respect to time, or reliable life:
-::<math>\hat{T}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>
-The corresponding confidence bounds are estimated from:
-::<math>\begin{align}
-  & {{T}_{U}}= & -\frac{1}{{{\lambda }_{L}}}\cdot \ln (R)+\hat{\gamma } \\
- & {{T}_{L}}= & -\frac{1}{{{\lambda }_{U}}}\cdot \ln (R)+\hat{\gamma }
-\end{align}</math>
-The same equations apply for the one-parameter exponential with <math>\gamma =0.</math>