norminvLibrary "norminv"
Description:
An inverse normal distribution is a way to work backwards
from a known probability to find an x-value. It is an informal term and
doesn't refer to a particular probability distribution. Returns the
value of the inverse normal distribution function for a specified value,
mean, and standard deviation.
Reference:
github.com
support.microsoft.com
norminv(x, mean, stdev)
Returns the value of the inverse normal distribution function for a specified value, mean, and standard deviation.
Parameters:
x : float, The input to the normal distribution function.
mean : float, The mean (mu) of the normal distribution function
stdev : float, The standard deviation (sigma) of the normal distribution function.
Returns: float.
Gauss
One-Sided Gaussian Filter w/ Channels [Loxx]One-Sided Gaussian Filter w/ Channels is a Gaussian Moving Average that is calculated using a Fibonacci weighting function. Keltner channels have been added to show zones of exhaustion. A better name would be "Half Gaussian bell weighted" or "Half normal distribution weighted" indicator, since the weights for calculation of the average (similar to linear weighted average) are taken from a normal distribution curve like function--but only the half of the curve is used for calculation.
Information of the Gaussian distribution can be found here : en.wikipedia.org and once you take a look at the standard normal distribution curve, it will be much clearer what is exactly done in this indicator.
After the Gaussian Filter is applied to the source input, an Ehlers' 2-Pole Super Smoother is applied to reduce noise without significant lag.
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Gaussian FilterGaussian Filter script.
This indicator was described by John F. Ehlers in his book "Rocket Science for Traders" (2001, Chapter 15: Infinite Impulse Response Filters).
Mean Reversion and Momentum - Updated with gaussiana smoothingMean Reversion and Momentum
Interpretation:
- Divergence means trend reversal
- Parallel movement means trend continuation
Squares above serve as a confirming signal
Gaussian Channel [DW]This study is an experiment utilizing the Ehlers Gaussian Filter technique combined with lag reduction techniques and true range to analyze trend activity.
Gaussian filters, as Ehlers explains it, are simply exponential moving averages applied multiple times.
First, beta and alpha are calculated based on the sampling period and number of poles specified. The maximum number of poles available in this script is 9.
Next, the data being analyzed is given a truncation option for reduced lag, which can be enabled with "Reduced Lag Mode".
Then the alpha and source values are used to calculate the filter and filtered true range of the dataset.
Filtered true range with a specified multiplier is then added to and subtracted from the filter, generating a channel.
Lastly, a one pole filter with a N pole alpha is averaged with the filter to generate a faster filter, which can be enabled with "Fast Response Mode".
Custom bar colors are included.
Note: Both the sampling period and number of poles directly affect how much lag the indicator has, and how smooth the output is.
Larger inputs will result in smoother outputs with increased lag, and smaller inputs will have noisier outputs with reduced lag.
For the best results, I recommend not setting the sampling period any lower than the number of poles + 1. Going lower truncates the equation.
NG [Gaussian Filter Multi-Pole]When smoothing data there is always a trade-off between lag and removal of noise.
Gaussian filter has a consistently low lag and a very smooth curve.
This filter works for poles higher than the 4 (usual usage).
Mathematically maximum poles is 15 after which coefficients are too high to see any difference.
By tuning Lag and number of Poles you can achieve a very smooth MA with least lag possible.
It's just as good as 3rd gen moving averages and can be used as input feed for other indicators.
