# Technical Studies Reference

### Double Stochastic - Bressert

This study calculates and displays a Bressert's Double Stochastic for the Price Data.

Let $$H$$, $$L$$, and $$C$$ be random variables denoting the High, Low, and Close Prices, respectively, and let $$H_t$$, $$L_t$$, and $$C_t$$ be their respective values at Index $$t$$. Let $$n_{HL}$$, $$n_{MA}$$, and $$n_S$$ be the High & Low Period Length, Stochastic Exponential Moving Average Length, and Smoothing Length Inputs, respectively. We then execute the first of two Fast %K and Fast %D calculations, which we denote as $$Fast\%K_t^{(1)}(n)$$ and $$Fast\%D_t^{(1)}(n,n_{MA})$$, respectively. It should be noted that our calculation of Fast% K is slightly different here than it is in the study KD - Fast. See that study for an explanation of the notation used in the following formulas.

$$Fast\%K_t^{(1)}(n_{HL}) = \displaystyle{Fast\%K_t(H,L,C,n) = \left\{ \begin{matrix} 100\cdot\frac{C_t - \min_t(L,n)}{\max_t(H,n) - \min_t(L,n)} & \max_t(H,n) - \min_t(L,n) \neq 0 \\ 0 & \max_t(H,n) - \min_t(L,n) = 0 \end{matrix}\right .}$$

$$Fast\%D_t^{(1)}(n_{HL},n_{MA}) = EMA_t\left(Fast\%K_t^{(1)}(n_{HL}), n_{MA}\right)$$

Note: $$Fast\%D_t^{(1)}(n_{HL},n_{MA})$$ is referred to as Double Stochastic (DS) Trigger.

Next we execute the second of two Fast %K and Fast %D calculations, which we denote as $$Fast\%K_t^{(2)}(n_{HL},n_{MA})$$ and $$Fast\%D_t^{(2)}(n_{HL},n_{MA})$$, respectively.

$$Fast\%K_t^{(2)}(n_{HL},n_{MA}) = Fast\%K_t\left(Fast\%D^{(1)}(n_{HL},n_{MA}), Fast\%D^{(1)}(n_{HL},n_{MA}), Fast\%D^{(1)}(n_{HL},n_{MA}), n_{HL}\right)$$

$$Fast\%D_t^{(2)}(n_{HL},n_{MA}) = EMA_t\left(Fast\%K^{(2)}(n_{HL},n_{MA}), n_{MA}\right)$$

Note: Both of the Fast %D calculations are done using Exponential Moving Averages instead of Simple Moving Averages. There is no Input to change this.

The value of the Double Stochastic - Bressert at Index $$t$$ is denoted as $$DS^{(B)}_t(n_{HL},n_{MA},n_S)$$, and is found by computing an Exponential Moving Average of this second Fast %D calculation.

$$DS^{(B)}_t(n_{HL},n_{MA},n_S) = EMA_t\left(Fast\%D^{(2)}(n_{HL},n_{MA}), n_S\right)$$

The Subgraph of both the Double Stochastic - Bressert and the DS Trigger are calculated and displayed for $$t \geq 0$$.

This study also displays horizontal lines at levels determined by the Upper Line Value and Lower Line Value Inputs.