Index of dispersion - Variance-to-Mean Ratio - VMR

As with the coefficient of variation, the index of dispersion is a ratio that is used to measure the dispersion of a probability distribution. It tells us whether prices or technical indicator values are dispersed or clustered compared to a standard statistical model.

Index of dispersion, also called dispersion index or variance to mean ratio, is a normalized measure unlike the standard deviation. It can be used, for example, to compare the volatility of different assets.

VMR (variance-to-mean ratio = index of dispersion) is equal to zero in the case of a constant random variable (not dispersed). It is equal to one in a Poisson distribution, higher than one in a negative binomial distribution (over dispersed) and between zero and one in a binomial distribution (under dispersed).

The function or trading indicator gets a time-series and a lookback period. Its formula consists of dividing the variance (Square of the standard deviation) by the mean. It is valid only when the mean is different from zero.

Example of its use:
a = close - sma(close, 30);
a = CoefficientDispersion(a, 30);
Plot(a, "");

The above formula displays on a chart the index of dispersion of the difference between the close price and the 30-Bar simple moving average.

Other Statistical Measures:
- The coefficient of variation can be downloaded here: Coefficient of Variation - Relative Standard Deviation.
- The coefficient of determination, which measure the relationship between two time-series, is available here: Coefficient of Determination - R Squared - Time-Series Prediction.

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