3.5.2.56 Wblfit

Definition:

wblfit(vX, a, b) uses Newton-Raphson method to calculate Maximum Likelihood Estimates (MLE) of a (scale) and b (shape) for Weibull distributed dataset vX.

The probability density function of Weibull distribution is

\[ba^{-b}x^{b -1} e^{-(\frac{x}{a})^b},\]

where a > 0 is scale and b > 0 is shape, with \(E(X)=a \Gamma \left(1+ \frac{1}{b}\right)\) and \(Var(X)=a ^2 \left \lbrack \Gamma \left(1+\frac{2}{b}\right) -\Gamma ^2 \left(1+\frac{1}{b} \right) \right \rbrack\) .

Parameters:

vX (input, vector)

input vector vX

a (output, double)

output scale parameter, \(a > 0\)

b (output, double)

output shape parameter, \(b > 0\)