Documentation

# wblfit

Weibull parameter estimates

## Syntax

parmhat = wblfit(data)
[parmhat,parmci] = wblfit(data)
[parmhat,parmci] = wblfit(data,alpha)
[...] = wblfit(data,alpha,censoring)
[...] = wblfit(data,alpha,censoring,freq)
[...] = wblfit(...,options)

## Description

parmhat = wblfit(data) returns the maximum likelihood estimates, parmhat, of the parameters of the Weibull distribution given the values in the vector data, which must be positive. parmhat is a two-element row vector: parmhat(1) estimates the Weibull parameter a, and parmhat(2) estimates the Weibull parameter b, in the pdf

$y=f\left(x|a,b\right)=b{a}^{-b}{x}^{b-1}{e}^{-{\left(\frac{x}{a}\right)}^{b}}{I}_{\left(0,\infty \right)}\left(x\right)$

[parmhat,parmci] = wblfit(data) returns 95% confidence intervals for the estimates of a and b in the 2-by-2 matrix parmci. The first row contains the lower bounds of the confidence intervals for the parameters, and the second row contains the upper bounds of the confidence intervals.

[[parmhat,parmci] = wblfit(data,alpha) returns 100(1 - alpha)% confidence intervals for the parameter estimates.

[...] = wblfit(data,alpha,censoring) accepts a Boolean vector, censoring, of the same size as data, which is 1 for observations that are right-censored and 0 for observations that are observed exactly.

[...] = wblfit(data,alpha,censoring,freq) accepts a frequency vector, freq, of the same size as data. The vector freq typically contains integer frequencies for the corresponding elements in data, but can contain any non-negative values. Pass in [] for alpha, censoring, or freq to use their default values.

[...] = wblfit(...,options) accepts a structure, options, that specifies control parameters for the iterative algorithm the function uses to compute maximum likelihood estimates. The Weibull fit function accepts an options structure that can be created using the function statset. Enter statset ('wblfit') to see the names and default values of the parameters that wblfit accepts in the options structure. See the reference page for statset for more information about these options.

## Examples

data = wblrnd(0.5,0.8,100,1);
[parmhat, parmci] = wblfit(data)
parmhat =
0.5861  0.8567
parmci =
0.4606  0.7360
0.7459  0.9973