# Bill Williams Alligator

### Description

This study calculates and displays the Bill Williams Alligator for the Price data. This study is a set of three indicators: the Jaw, Teeth, and Lips of the Alligator. It is closely related to the Smoothed Moving Average. See that study for an explanation of the notation used here.

Let the Jaw Length, Teeth Length, and Lips Length Inputs be denoted as $$n_J$$, $$n_T$$, and $$n_L$$, respectively. We denote the Jaw, Teeth, and Lips of the Bill Williams Alligator at Index $$t$$ as $$Jaw_t(X,n_J)$$, $$Teeth_t(X,n_T)$$, and $$Lips_t(X,n_L)$$, respectively, and we compute them as follows.

For $$t \geq 8$$: $$Jaw_t(X,n_J) = SMMA_{t - 8}(X,n_J,0)$$

For $$t \geq 5$$: $$Teeth_t(X,n_T) = SMMA_{t - 5}(X,n_T,0)$$

For $$t \geq 3$$: $$Lips_t(X,n_L) = SMMA_{t - 3}(X,n_L,0)$$

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