# ks.gumbel: Test of Kolmogorov-Smirnov for the Gumbel distribution In reliaR: Package for some probability distributions.

## Description

The function `ks.gumbel()` gives the values for the KS test assuming a Gumbel with shape parameter mu and scale parameter sigma. In addition, optionally, this function allows one to show a comparative graph between the empirical and theoretical cdfs for a specified data set.

## Usage

 ```1 2``` ```ks.gumbel(x, mu.est, sigma.est, alternative = c("less", "two.sided", "greater"), plot = FALSE, ...) ```

## Arguments

 `x` vector of observations. `mu.est` estimate of the parameter mu `sigma.est` estimate of the parameter sigma `alternative` indicates the alternative hypothesis and must be one of `"two.sided"` (default), `"less"`, or `"greater"`. `plot` Logical; if TRUE, the cdf plot is provided. `...` additional arguments to be passed to the underlying plot function.

## Details

The Kolmogorov-Smirnov test is a goodness-of-fit technique based on the maximum distance between the empirical and theoretical cdfs.

## Value

The function `ks.gumbel()` carries out the KS test for the Gumbel

## References

Marshall, A. W., Olkin, I.(2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families, Springer, New York.

`pp.gumbel` for `PP` plot and `qq.gumbel` for `QQ` plot

## Examples

 ```1 2 3 4 5 6 7``` ```## Load data sets data(dataset2) ## Maximum Likelihood(ML) Estimates of mu & sigma for the data(dataset2) ## Estimates of mu & sigma using 'maxLik' package ## mu.est = 212.157, sigma.est = 151.768 ks.gumbel(dataset2, 212.157, 151.768, alternative = "two.sided", plot = TRUE) ```

### Example output

```	One-sample Kolmogorov-Smirnov test

data:  x
D = 0.069896, p-value = 0.6501
alternative hypothesis: two-sided

Warning message:
In ks.test(x, pgumbel, mu, sigma, alternative = alternative) :
ties should not be present for the Kolmogorov-Smirnov test
```

reliaR documentation built on May 29, 2017, 12:34 p.m.