# Documentation

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# 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 `lognfit` 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```