R: One-sample Kolmogorov-Smirnov test for student-t distribution

ks_test_t {LambertW} | R Documentation

## One-sample Kolmogorov-Smirnov test for student-t distribution

### Description

Performs a two-sided KS test for H_0: X \sim t_{ν} with c, scale s, and degrees of freedom ν. If parameters are not specified, the MLE given the data will be used (see `fitdistr`).

For estimated parameters of the t-distribution the p-values are incorrect and should be adjusted. See `ks.test` and the references therein (Durbin (1973)). As a more practical approach consider bootstrapping and estimating the p-value empirically.

### Usage

    ks_test_t(x, param = NULL)

### Arguments

`x` | a numeric vector of data values.
`param` | 3-dimensional named vector `('location', 'scale', 'df')` which parametrizes the student t distribution. Default: `param = NULL`, in which case it will be estimated from `x`.

### Value

A list of class `"htest"` containing:

`statistic` | the value of the Kolomogorv-Smirnov statistic.
`p.value` | the p-value for the test.
`alternative` | a character string describing the alternative hypothesis.
`method` | the character string "One-sample Kolmogorov-Smirnov test student-t" plus rounded parameter values.
`data.name` | a character string giving the name(s) of the data.

### See Also

`fitdistr`, `ks.test`

### Examples

    set.seed(1021)
    beta.true <- c(location = 0, scale = 1, df = 4)
    xx <- rt(n = 1000, df = beta.true['df'])
    ks_test_t(xx)
    ks_test_t(xx, beta.true)

[Package LambertW version 0.6.7 Index]