# Quantiles and probabilities of p-variation

### Description

The distribution of p-variation of `BridgeT(x)`

depends on `n=length(x)`

.
This fact is important for getting appropriate quantiles (or p-value).
These functions helps to deal with it.

### Usage

1 2 3 4 5 6 7 8 9 | ```
PvarQuantile(n, prob = c(0.9, 0.95, 0.99), DF = PvarQuantileDF)
PvarPvalue(n, stat, DF = PvarQuantileDF)
getMean(n, bMean = MeanCoef)
getSd(n, bSd = SdCoef)
NormalisePvar(x, n, bMean = MeanCoef, bSd = SdCoef)
``` |

### Arguments

`n` |
a positive integer indicating the length of data vector. |

`prob` |
cumulative probabilities of p-variation distribution. |

`DF` |
a |

`stat` |
a vector of p-variation statistics. |

`bMean` |
a coefficient vector that defines a function of the mean of p-variation. |

`bSd` |
a coefficient vector that defines a function of the standard deviation of p-variation. |

`x` |
a numeric vector of data values. |

### Details

The distribution of p-variance is form Monte-Carlo simulation based on 140 millions iterations.
The data frame `PvarQuantileDF`

saves the results of Monte-Carlo simulation.

Meanwhile, `MeanCoef`

and `SdCoef`

defines the coefficients of functional
form (conditional on `n`

) of `mean`

and `sd`

statistics.

A functional form of `mean`

and `sd`

statistics are the same, namely

*
f(n) = b_1 + b_2 * n^b_2 .
*

The coefficients *(b_1, b_2, b_3)* are saved in vectors `MeanCoef`

and `SdCoef`

.
Those vectors are estimated with `nls`

function form Monte-Carlo simulation.

### Value

Functions `PvarQuantile`

and `PvarPvalue`

returns a corresponding value quantile or the probability.
Functions `getMean`

and `getSd`

returns a corresponding value of `mean`

and `sd`

statistics.
Function `NormalisePvar`

returns normalize values.

### Note

Arguments `n`

, `stat`

and `prob`

might be vectors,
but they can't be vectors simultaneously (at least one of then must be a number).

### See Also

`PvarBreakTest`

, `PvarQuantileDF`

,
`NormalisePvar`

, `getMean`

, `getSd`