1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.6. Gallery of Distributions
1.3.6.6.8. |
Weibull Distribution |
where 
is the
shape parameter,
is the
location parameter and
is the
scale parameter. The case where
= 0 and
= 1 is called the
standard Weibull distribution. The case where
= 0 is called the
2-parameter Weibull distribution. The equation for the standard
Weibull distribution reduces to
Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function.
The following is the plot of the Weibull probability density function.
The following is the plot of the Weibull cumulative distribution
function with the same values of
as the pdf plots above.
The following is the plot of the Weibull percent point function with
the same values of as the pdf
plots above.
The following is the plot of the Weibull hazard function with the
same values of as the pdf plots
above.
The following is the plot of the Weibull cumulative hazard function
with the same values of as the
pdf plots above.
The following is the plot of the Weibull survival function
with the same values of as
the pdf plots above.
The following is the plot of the Weibull inverse survival function
with the same values of as the
pdf plots above.
| Mean |
where
|
| Median |
|
| Mode |
|
| Range | Zero to positive infinity. |
| Standard Deviation |
![SQRT[GAMMA((gamma+2)/gamma) - (GAMMA((gamma+1)/gamma))**2]](eqns/weisd.gif)
|
| Coefficient of Variation |
|
is the gamma
function
![GAMMA(a) = INTEGRAL[t**(a-1)*EXP(-t)dt] where the
integration is from 0 to infinity](eqns/gammfunc.gif)
