3.5.3.1.27 Wblcdf

Definition:

\(prob = wblcdf(x, a, b)\) computes the low tail Weibull cumulative distribution function for value \(x\) using the parameters \(a\) and \(b\).

The low tail Weibull cumulative distribution function is defined by: \( P(X<x|a,b)=\int_0^xba^{-b}t^{b-1}e^{-(\frac ta)^b}dt=1-e^{-(\frac xa)^b}I_{(0,+\infty )}(x)\)

where \(I_{(0,+\infty )}(x)\) is the interval on which the Weibull CDF is not zero.

Parameters:

x (input, double)

the value of the \(x\) variate.\(x\geq 0\)

a (input, double)

the scale parameter, \(a\), of the required Weibull distribution, must be positive( \(a>0\) ).

b (input, double)

the shape parameter, \(b\), of the required Weibull distribution, must be positive ( \(b>0\) ) .

prob (output, double)

the probability.