• Technical Studies Reference
• Common Study Inputs (Opens a new page)
• Using Studies (Opens a new page)

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.

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 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.