# Technical Studies Reference

### Normalized Volume

This study calculates and displays a Normalized Volume.

Let $$V$$ be a random variable denoting the Volume, and let $$V_t$$ be the value of the Volume at Index $$t$$. Let the Input Length be denoted as $$n$$. Then we denote the Normalized Volume at Index $$t$$ for the given Inputs as $$V^{(N)}_t(n)$$, and we compute it in terms of a Simple Moving Average for $$t \geq n - 1$$ as follows.

$$\displaystyle{V^{(N)}_t(n) =\left\{ \begin{matrix} 100\cdot\frac{V_t}{SMA_t(V,n)} & SMA_t(V,n) \neq 0 \\ V^{(N)}_{t-1}(n) & SMA_t(V,n) = 0 \end{matrix}\right .}$$

Note: Depending on the setting of the Input Moving Average Type, the Simple Moving Average in the above formula could be replaced with an Exponential Moving Average, a Linear Regression Moving Average, a Weighted Moving Average, a Wilders Moving Average, a Simple Moving Average - Skip Zeros, or a Smoothed Moving Average.

This study also displays horizontal lines at levels determined by the High Volume and Low Volume Inputs.