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### Stochastic - Percentile

This study calculates and displays the percentile rank of the data specified by the **Input Data** Input. The ranking is done over a moving window whose size is specified by the **Length** Input. This study also calculates and displays a moving average of the percentile rank. This indicator was developed by Peter Worden, and is sometimes referred to as a Worden Stochastic.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of the **Input Data** at Index \(t\). Let the Input **Length** be denoted as \(n\).

At Index \(t\), the \(n\) values \(X_{t - n + 1},...,X_t\) of the **Input Data** are arranged in ascending order and ranked from lowest to highest, starting with a Rank of \(0\) and going up to a Rank of \(n - 1\). The Rank of the most recent value of \(X\) at Index \(t\) for the given **Length** is denoted as \(R_t(X,n)\).

We denote the value of the **Stochastic - Percentile** at Index \(t\) for the given Inputs as \(SP_t(X,n)\), and we compute it for \(t \geq n - 1\) as follows.

**Note**: We perform the following internal calculations for \(0 \leq t < n - 1\). These values are not displayed as output.

Let the **Moving Average Length** Input be denoted as \(n_{MA}\). Then we denote the Moving Average of **Stochastic - Percentile** at Index \(t\) for the given Inputs as \(\overline{SP}_t(X,n,n_{MA})\), and we compute it in terms of a Simple Moving Average for \(t \geq n - 1\) as follows.

In the above formula, \(SP(X,n)\) is a random variable denoting the **Stochastic - Percentile** of **Length** \(n\) for the **Input Data** \(X\).

In addition to the graphs of \(SP_t(X,n)\) and \(\overline{SP}_t(X,n,n_{MA})\), this study also displays two horizontal lines whose levels are determined by the Inputs **Line 1 Value** and **Line 2 Value**.

#### Inputs

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Wednesday, 03rd January, 2018.