# 3.5.2.43 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, $b > 0$