OPEN-SOURCE SCRIPT

Median of Means Estimator

Actualizado
Median of Means (MoM) is a measure of central tendency like mean (average) and median. However, it could be a better and robust estimator of central tendency when the data is not normal, asymmetric, have fat tails (like stock price data) and have outliers. The MoM can be used as a robust trend following tool and in other derived indicators.

Median of means (MoM) is calculated as follows, the MoM estimator shuffles the "n" data points and then splits them into k groups of m data points (n= k*m). It then computes the Arithmetic Mean of each group (k). Finally, it calculate the median over the resulting k Arithmetic Means. This technique diminishes the effect that outliers have on the final estimation by splitting the data and only considering the median of the resulting sub-estimations. This preserves the overall trend despite the data shuffle.
Below is an example to illustrate the advantages of MoM
Set A Set B Set C
3 4 4
3 4 4
3 5 5
3 5 5
4 5 5
4 5 5
5 5 5
5 5 5
6 6 8
6 6 8
7 7 10
7 7 15
8 8 40
9 9 50
10 100 100

Median 5 5 5
Mean 5.5 12.1 17.9
MoM 5.7 6.0 17.3

For all three sets the median is the same, though set A and B are the same except for one outlier in set B (100) it skews the mean but the median is resilient. However, in set C the group has several high values despite that the median is not responsive and still give 5 as the central tendency of the group, but the median of means is a value of 17.3 which is very close to the group mean 17.9. In all three cases (set A, B and C) the MoM provides a better snapshot of the central tendency of the group. Note: The MoM is dependent on the way we split the data initially and the value might slightly vary when the randomization is done sevral time and the resulting value can give the confidence interval of the MoM estimator.
Notas de prensa
Updated default length to 15 use lengths which are multiples of 3.
Notas de prensa
minor update
educationalmeanmedianMoving Averagesrobuststatistics

Script de código abierto

Siguiendo fielmente el espíritu de TradingView, el autor de este script lo ha publicado en código abierto, permitiendo que otros traders puedan entenderlo y verificarlo. ¡Olé por el autor! Puede utilizarlo de forma gratuita, pero tenga en cuenta que la reutilización de este código en la publicación se rige por las Normas internas. Puede añadir este script a sus favoritos y usarlo en un gráfico.

¿Quiere utilizar este script en un gráfico?

Exención de responsabilidad