# gamfit

Gamma parameter estimates

## Syntax

```phat = gamfit(data) [phat,pci] = gamfit(data) [phat,pci] = gamfit(data,alpha) [...] = gamfit(data,alpha,censoring,freq,options) ```

## Description

`phat = gamfit(data)` returns the maximum likelihood estimates (MLEs) for the parameters of the gamma distribution given the data in vector `data`.

`[phat,pci] = gamfit(data)` returns MLEs and 95% percent confidence intervals. The first row of `pci` is the lower bound of the confidence intervals; the last row is the upper bound.

`[phat,pci] = gamfit(data,alpha)` returns `100(1 - alpha)`% confidence intervals. For example, `alpha` = `0.01` yields 99% confidence intervals.

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

`[...] = gamfit(data,alpha,censoring,freq)` accepts a frequency vector of the same size as `data`. `freq` typically contains integer frequencies for the corresponding elements in `data`, but may contain any nonnegative values.

`[...] = gamfit(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. The gamma fit function accepts an `options` structure which can be created using the function `statset`. Enter `statset('gamfit')` to see the names and default values of the parameters that `gamfit` accepts in the `options` structure.

## Examples

Fit a gamma distribution to random data generated from a specified gamma distribution:

```a = 2; b = 4; data = gamrnd(a,b,100,1); [p,ci] = gamfit(data) p = 2.1990 3.7426 ci = 1.6840 2.8298 2.7141 4.6554```

## References

 Hahn, Gerald J., and S. S. Shapiro. Statistical Models in Engineering. Hoboken, NJ: John Wiley & Sons, Inc., 1994, p. 88.