# StatisticsPvarBreakTest: Quantiles and probabilities of p-variation In pvar: Calculation and Application 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 `data.frame` that links `prob` and `stat` . `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).

`PvarBreakTest`, `PvarQuantileDF`, `NormalisePvar`, `getMean`, `getSd`