Calculation of Weibull distribution

Keyword

Weibull distribution,Probability density function,Cumulative density function,Shape parameter,Location parameter,Scale parameter,Mean,Median,Mode,Variance,Gamma Function.

Reference

[1]:Weibull Distribution:NIST/SEMATECH e-Handbook of Statistical Methods
[2]:Horst Rinne:『The Weibull Distribution: A Handbook 』,p.43.
[3]:Weibull distribution:Wikipedia

Remarks

・γ:Shape parameter , μ:location parameter , α:scale parameter.
・LaTex: \\f\left ( x \right )=\frac{\gamma }{\alpha }\left ( \frac{x-\mu }{\alpha } \right )^{\gamma -1}exp\left ( -\left ( \frac{x-\mu }{\alpha } \right ) ^{\gamma }\right )\\F\left ( x \right )=1-exp\left (-\left ( \frac{x-\mu }{\alpha } \right ) ^{\gamma } \right )\\\gamma :\textup{shape parameter}\, ,\alpha :\textup{scale parameter}\\\mu :\textup{location parameter}
・Making above Equation Image is powered by CODECOGS

History

・2010/05/21:Upload.