# Normalization functions

The following functions can be used for normalizing and compressing time series
or indicator values to a range that's independent of the asset and time frame.
They suppress long-term trend and emphasize short cycles in various ways. Normalization is often required for machine learning algorithms.
## center (var Value, int TimePeriod): var

Centers **Value** by subtracting its median over the **TimePeriod**. Using the median instead of the mean reduces the effect of outliers.
## compress (var Value, int TimePeriod): var

Compresses **Value** to the -100...+100 range. For this, **Value** is divided by its interquartile range - the difference of the 75th and 25th percentile - taken over **TimePeriod**, and then compressed by a cdf function. Works best when **Value** is an oscillator that crosses the zero line. Formula: **200 * cdf(0.25*Value/(P75-P25)) - 100**.
## scale (var Value, int TimePeriod): var

Centers and compresses **Value** to the -100...+100 scale. The deviation of **Value** from its median is divided by its interquartile range and then compressed by a cdf function. Formula: **200 * cdf(0.5*(Value-Median)/(P75-P25)) - 100**.
## normalize (var Value, int TimePeriod): var

Normalizes **Value** to the -100...+100 range by subtracting its minimum and dividing by its range over **TimePeriod**. Formula: **200 * (Value-Min)/(Max-Min) - 100 **.
For a 0..100 oscillator, multiply the returned value with 0.5 and add 50.
## zscore (var Value, int TimePeriod): var

Calculates the Z-score of the **Value**. The Z-score is the deviation from the mean over the **TimePeriod**, divided by the standard deviation. Formula: **(Value-Mean)/StdDev**.

### Parameters:

**Value** - Variable, expression, or indicator to be normalized.

**TimePeriod** - Normalization period.
### Returns:

Normalized **Value**.
### Remarks:

- The above functions generate series (see remarks).
- For converting a value
**X** from a -100.+100 range to a
0...**Y** range, use the expression **Y*(X+100)/200**.
- There are other functions for compressing data series in various ways:
tanh compresses to the -1..1 range,
**sigmoid** (= **1./(1.+exp(-x))** ) compresses to the 0..1 range,
Normalize and AGC compress
data series to -1..+1, PercentRank compresses to 0..100, and FisherN compresses so that most values fall inside -1.5..+1.5.

### Example:

function run()
{
set(PLOTNOW);
PlotWidth = 600;
PlotHeight1 = PlotHeight2;
PlotBars = 400;
LookBack = 200;
var ATR100 = ATR(100);
plot("ATR 100",ATR100,NEW,RED);
plot("center",center(ATR100,100),NEW,RED);
plot("compress",compress(ATR100-0.003,100),NEW,RED);
plot("scale",scale(ATR100,100),NEW,RED);
plot("normalize",normalize(ATR100,100),NEW,RED);
plot("zscore",zscore(ATR100,100),NEW,RED);
}

### See also:

AGC, FisherN, advise, cdf

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