Template:Lognormal distribution statistical properties: Difference between revisions

Latest revision as of 04:44, 13 August 2012

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-==Lognormal Statistical Properties==
+#REDIRECT [[Lognormal Distribution Functions]]
-{{ld mean}}
-{{ld median}}
-{{ld mode}}
-{{ld standard deviation}}
-{{ld lognormal reliability function}}
-{{ld lognormal conditional reliability}}
-===The Lognormal Reliable Life===
-As there is no closed-form solution for the lognormal reliability equation, no closed-form solution exists for the lognormal reliable life either.  In order to determine this value, one must solve the equation:
-::<math>{{R}_{T}}=\int_{\text{ln}(T)}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{s-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}ds</math>
-for <math>T</math> .
-===The Lognormal Failure Rate Function===
-The lognormal failure rate is given by:
-::<math>\lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{T\cdot {{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{(\tfrac{{T}'-{\mu }'}{{{\sigma }_{{{T}'}}}})}^{2}}}}}{\int_{{{T}'}}^{\infty }\tfrac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{(\tfrac{t-{\mu }'}{{{\sigma }_{{{T}'}}}})}^{2}}}}dt}</math>
-As with the reliability equations, standard normal tables will be required to solve for this function.