Template:Gamma mean median and mode: Difference between revisions
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(Created page with '===The Gamma Mean, Median and Mode=== The gamma mean or MTTF is: ::<math>\overline{T}=k{{e}^{\mu }}</math> The mode exists if <math>k>1</math> and is given by: ::<math>\t…') |
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===The Gamma Mean, Median and Mode=== | ===The Gamma Mean, Median and Mode=== | ||
The gamma mean or MTTF is: | The gamma mean or MTTF is: | ||
::<math>\overline{T}=k{{e}^{\mu }}</math> | ::<math>\overline{T}=k{{e}^{\mu }}</math> | ||
The mode exists if <math>k>1</math> and is given by: | The mode exists if <math>k>1</math> and is given by: | ||
::<math>\tilde{T}=(k-1){{e}^{\mu }}</math> | ::<math>\tilde{T}=(k-1){{e}^{\mu }}</math> | ||
The median is: | The median is: | ||
::<math>\widehat{T}={{e}^{\mu +\ln (\Gamma _{ | ::<math>\widehat{T}={{e}^{\mu +\ln (\Gamma _{I}^{-1}(0.5;k))}}</math> | ||
Revision as of 22:16, 14 February 2012
The Gamma Mean, Median and Mode
The gamma mean or MTTF is:
- [math]\displaystyle{ \overline{T}=k{{e}^{\mu }} }[/math]
The mode exists if [math]\displaystyle{ k\gt 1 }[/math] and is given by:
- [math]\displaystyle{ \tilde{T}=(k-1){{e}^{\mu }} }[/math]
The median is:
- [math]\displaystyle{ \widehat{T}={{e}^{\mu +\ln (\Gamma _{I}^{-1}(0.5;k))}} }[/math]