Statistics with Calculator-style Summation Registers

Statistics of list of (x, y) pairs from calculator-style summation registers.

CONTENTS

Statistics with Calculator-style Summation Registers

Why use this package?

Use this package to obtain summary statistics of a list of $(x, y)$ pairs when the pairs are presented in sequence, such as from a control system. It is not necessary to retain the entire list in memory, this package will retain the cumulative values necessary to compute all analytical results.

There are no external dependencies on add-on packages such as numpy or scipy. Only the math package from the Python Standard Library is used.

Statistics may be calculated at any time from the summation registers.

The $(x, y)$ values may be entered in any order. It is not necessary to sort them.

Examples

In [1]: import pysumreg

In [2]: reg = pysumreg.SummationRegisters()

mean and standard deviation

In [3]: reg.clear()
   ...: reg.add(1, -1)
   ...: reg.add(2, -2)
   ...: reg.add(3, -3)
   ...: print(f"{reg.mean_x=}")
   ...: print(f"{reg.stddev_x=}")
   ...: print(f"{reg.mean_y=}")
   ...: print(f"{reg.stddev_y=}")
   ...: print(f"{reg.min_x=}")
   ...: print(f"{reg.max_x=}")
   ...: print(f"{reg.min_y=}")
   ...: print(f"{reg.max_y=}")
   ...: print(f"{reg.x_at_max_y=}")
   ...: print(f"{reg.x_at_min_y=}")
   ...: 
reg.mean_x=2.0
reg.stddev_x=1.0
reg.mean_y=-2.0
reg.stddev_y=1.0
reg.min_x=1
reg.max_x=3
reg.min_y=-3
reg.max_y=-1
reg.x_at_max_y=1
reg.x_at_min_y=3

linear regression & correlation coefficient

In [4]: reg.clear()
   ...: reg.add(1, -1)
   ...: reg.add(2, -2)
   ...: reg.add(3, -3)
   ...: print(f"{reg.correlation=}")
   ...: print(f"{reg.intercept=}")
   ...: print(f"{reg.slope=}")
   ...: 
reg.correlation=-1.0
reg.intercept=0.0
reg.slope=-1.0

peak analysis: centroid and width of x weighted by y

In [5]: reg.clear()
   ...: reg.add(1, 0)
   ...: reg.add(2, 1)
   ...: reg.add(3, 0)
   ...: print(f"{reg.max_y=}")
   ...: print(f"{reg.centroid=}")
   ...: print(f"{reg.sigma=}")
   ...: 
reg.max_y=1
reg.centroid=2.0
reg.sigma=0.0

In [6]: reg.add(1.5, 0.5)
   ...: reg.add(2.5, 0.5)
   ...: print(f"{reg.max_y=}")
   ...: print(f"{reg.centroid=}")
   ...: print(f"{reg.sigma=}")
   ...: 
reg.max_y=1
reg.centroid=2.0
reg.sigma=0.3535533905932738