# Documentation

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# normfit

Normal parameter estimates

## Syntax

`[muhat,sigmahat] = normfit(data)[muhat,sigmahat,muci,sigmaci] = normfit(data)[muhat,sigmahat,muci,sigmaci] = normfit(data,alpha)[...] = normfit(data,alpha,censoring)[...] = normfit(data,alpha,censoring,freq)[...] = normfit(data,alpha,censoring,freq,options)`

## Description

`[muhat,sigmahat] = normfit(data)` returns an estimate of the mean μ in `muhat`, and an estimate of the standard deviation σ in `sigmahat`, of the normal distribution given the data in `data`.

`[muhat,sigmahat,muci,sigmaci] = normfit(data)` returns 95% confidence intervals for the parameter estimates on the mean and standard deviation in the arrays `muci` and `sigmaci`, respectively. The first row of `muci` contains the lower bounds of the confidence intervals for μ the second row contains the upper bounds. The first row of `sigmaci` contains the lower bounds of the confidence intervals for σ, and the second row contains the upper bounds.

`[muhat,sigmahat,muci,sigmaci] = normfit(data,alpha)` returns 100(1 - `alpha`) % confidence intervals for the parameter estimates, where `alpha` is a value in the range `[0 1]` specifying the width of the confidence intervals. By default, `alpha` is `0.05`, which corresponds to 95% confidence intervals.

`[...] = normfit(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. `data` must be a vector in order to pass in the argument `censoring`.

`[...] = normfit(data,alpha,censoring,freq)` accepts a frequency vector, `freq`, of the same size as `data`. Typically, `freq` contains integer frequencies for the corresponding elements in `data`, but can contain any nonnegative values. Pass in `[]` for `alpha`, `censoring`, or `freq` to use their default values.

`[...] = normfit(data,alpha,censoring,freq,options)` accepts a structure, `options`, that specifies control parameters for the iterative algorithm the function uses to compute maximum likelihood estimates when there is censoring. The normal fit function accepts an `options` structure which you can create using the function `statset`. Enter `statset('normfit')` to see the names and default values of the parameters that `normfit` accepts in the `options` structure. See the reference page for `statset` for more information about these options.

 Note:   With no censoring, `normfit` computes `muhat` using the sample mean and `sigmahat` using the square root of the unbiased estimator of the variance. With censoring, both `muhat` and `sigmahat` are the maximum likelihood estimates.

## Examples

In this example the data is a two-column random normal matrix. Both columns have µ = 10 and σ = 2. Note that the confidence intervals below contain the "true values."

```data = normrnd(10,2,100,2); [mu,sigma,muci,sigmaci] = normfit(data) mu = 10.1455 10.0527 sigma = 1.9072 2.1256 muci = 9.7652 9.6288 10.5258 10.4766 sigmaci = 1.6745 1.8663 2.2155 2.4693```