# Computation of the Permutation Distribution

### Description

Methods for computation of the density function, distribution function, quantile function, random numbers and support of the permutation distribution.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
## S4 method for signature 'AsymptNullDistribution'
dperm(object, x, ...)
## S4 method for signature 'IndependenceTest'
dperm(object, x, ...)
## S4 method for signature 'NullDistribution'
dperm(object, x, ...)
## S4 method for signature 'AsymptNullDistribution'
pperm(object, q, ...)
## S4 method for signature 'IndependenceTest'
pperm(object, q, ...)
## S4 method for signature 'NullDistribution'
pperm(object, q, ...)
## S4 method for signature 'AsymptNullDistribution'
qperm(object, p, ...)
## S4 method for signature 'IndependenceTest'
qperm(object, p, ...)
## S4 method for signature 'NullDistribution'
qperm(object, p, ...)
## S4 method for signature 'IndependenceTest'
rperm(object, n, ...)
## S4 method for signature 'NullDistribution'
rperm(object, n, ...)
## S4 method for signature 'IndependenceTest'
support(object, ...)
## S4 method for signature 'NullDistribution'
support(object, ...)
``` |

### Arguments

`object` |
an object from which the density function, distribution function, quantile function, random numbers or support of the permutation distribution can be computed. |

`x, q` |
a numeric vector, the quantiles for which the density function or distribution function is computed. |

`p` |
a numeric vector, the probabilities for which the quantile function is computed. |

`n` |
a numeric vector, the number of observations. If |

`...` |
further arguments to be passed to methods. |

### Details

The methods `dperm`

, `pperm`

, `qperm`

, `rperm`

and
`support`

compute the density function, distribution function, quantile
function, random deviates and support, respectively, of the permutation
distribution.

### Value

The density function, distribution function, quantile function, random
deviates or support of the permutation distribution computed from
`object`

. A numeric vector.

### Note

The density of asymptotic permutation distributions for maximum-type tests or
exact permutation distributions obtained by the split-up algoritm is reported
as `NA`

. The quantile function of asymptotic permutation distributions
for maximum-type tests cannot be computed for `p`

less than 0.5, due to
limitations in the mvtnorm package. The support of exact permutation
distributions obtained by the split-up algorithm is reported as `NA`

.

In versions of coin prior to 1.1-0, the support of asymptotic
permutation distributions was given as an interval containing 99.999 % of the
probability mass. It is now reported as `NA`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
## Two-sample problem
dta <- data.frame(
y = rnorm(20),
x = gl(2, 10)
)
## Exact Ansari-Bradley test
at <- ansari_test(y ~ x, data = dta, distribution = "exact")
## Support of the exact distribution of the Ansari-Bradley statistic
supp <- support(at)
## Density of the exact distribution of the Ansari-Bradley statistic
dens <- dperm(at, supp)
## Plotting the density
plot(supp, dens, type = "s")
## 95 % quantile
qperm(at, 0.95)
## One-sided p-value
pperm(at, statistic(at))
## Random number generation
rperm(at, 5)
``` |