30.1.182 WeibullCDF

1 Function
2 Brief Description
3 Sample Curve
4 Parameters
5 Derived Parameters
6 Script Access
7 Function File
8 Category

Function

$y=\begin{cases} y_0+A_1\int_{0}^{x}ba^{-b}t^{b-1}e^{-\left (\frac{t}{a}\right)^b}dt=y_0+A_1\left ( 1- e^{-\left (\frac{x}{a}\right)^b}\right )&x>0\\ y_0 & x\leq 0 \end{cases}$

Brief Description

Weibull cumulative distribution function

Sample Curve

Parameters

Number: 4

Names: y0, A1, a, b

Meanings: y0 = offset, A1 = Amplitude, a = Scale, b = Shape

Lower Bounds: A1 > 0.0, a > 0.0, b> 0.0

Upper Bounds: none

Derived Parameters

Mean: mu=a*gamma(1+1/b)

Standard Deviation: sigma=a*sqrt( gamma(1+2/b)-(gamma(1+1/b))^2 )

Script Access

 wblcdf(x, a, b)

Function File

FITFUNC\WeibullCDF.fdf