# Technical Studies Reference

### Positive Volume Index

This study calculates and displays the Positive Volume Index (PVI) for the Volume data and the data specified by the Input Data Input. This study uses the version of the PVI created by Norman G. Fosback.

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 Initial Value be denoted as $$PVI_0$$. Then we denote the Positive Volume Index for the given Inputs at Index $$t$$ as $$PVI_t(X,PVI_0)$$, and we compute it for $$t \geq 0$$ as follows.

For $$t = 0$$: $$PVI_0(X,PVI_0) = PVI_0$$

For $$t > 0$$: $$\displaystyle{PVI_t(X,PVI_0) = \left\{ \begin{matrix} PVI_{t - 1}(X,PVI_0) + \frac{X_t - X_{t - 1}}{X_{t - 1}}\cdot PVI_{t - 1}(X,PVI_0) & V_t > V_{t - 1} \\ PVI_{t - 1}(X,PVI_0) & V_t \leq V_{t - 1} \end{matrix}\right .}$$

#### Inputs

• Input Data
• Initial Value:The initial starting value for the study. This value should be close to the average price of the symbol to allow the study to be overlaid on the main price graph.