Table of Contents

#include <moment.h> void ini_moment(m, mom, ndat)void accum_moment(m, x, w)void decr_moment(m, x, w)void reset_moment(m) real show_moment(m, mom)int n_moment(m)real sum_moment(m)real sratio_moment(m)real mean_moment(m)real median_moment(m)real sigma_moment(m)real skewness_moment(m)real kurtosis_moment(m)real h3_moment(m)real h4_moment(m)real mad_moment(m)real mard_moment(m) real min_moment(m);real max_moment(m); void compute_robust_moment(m);int n_robust_moment(m);real min_robust_moment(m);real max_robust_moment(m);real mean_robust_moment(m);real median_robust_moment(m);real sigma_robust_moment(m); Moment *m;int mom, ndat;real x, w;

If only a datamin/max is needed, setting **mom<0**
can be used to prevent the more expensive moment calculations.

Moving or
running averages (or moments) can be done by supplying **ndat>0** to ini_moment.
It will keep a memory of the last **ndat** data values and the moments now
become running moments.

Note that the *median_moment* can only be used in
**x** (the weights are ignored) and moving moment where **ndat>0**.

**mean_moment** returns
the mean value, where **sigma_moment** returns the square root of the variance

**sratio_moment** returns a measure of how much signal there is compared to
the noise, by compting (SumP+SumN)/(SumP-SumN). For pure noise this should
be near 0, and for pure signal, where SumN=0, near 1.

**robust_moment’s** can
also be computed. These are based on an algorithm to remove the outliers.
It first computes the distance between the 1st and 3rd quartile, then removes
all points further than 1.5 times that distance from the 1st and 3rd quartile.
After calling **compute_robust_moment**, the mean, median and sigma can be
retrieved as those computations are done in a temporary Moment structure.
Caveat: for large datasets and/or moving moments, robust_moment’s can become
expensive because of the need for sorting to get the quartiles.

**mad_moment**
computes the Median Absolute Deviation (MAD), arguably a better measure
for the Standard Deviation. As with the robust moments, it needs to keep
a copy of the data available. MAD is formally RMS/1.4826. Related is **mard_moment**,
the Mean Absolute Relative Difference (MARD).

real x[100], w[100]; int i,n=100; Moment m; ... ini_moment(&m,2,0); /* up to 2nd order moment, and using no circular buffer */ for (i=0; i<n; i)accum_moment(&m,x[i],w[i]); printf("Mean: %g Dispersion: %g\n",mean_moment(&m), sigma_moment(&m)); compute_robust_moment(&m); printf("Robust Mean: %g Dispersion: %g\n",mean_robust_moment(&m), sigma_robust_moment(&m));

typedef struct {from the standard include fileint mom;int n;real *sum;real datamin, datamax;int ndat;int idat;real *dat;real *sum; } Moment;

http://apophenia.info

~/src/kernel/miscmoment.c

30-oct-93CreatedPJT 8-nov-93fixed init bugPJT 13-jun-95added decr_momentPJT 2-feb-05added moving momentsPJT 2-mar-11added h3,h4PJT 24-apr-13documented robust statisticsPJT 16-jan-14added MADPJT 11-jun-14clarified MAD and MARD (the old MAD was really MARD)PJT 12-jul-20added min/max for robust momentPJT 14-nov-21added sratioPJT