wiki:TallyCowan

Version 2 (modified by cowan, 4 years ago) (diff)

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Introduction

A tally is a member of a disjoint type whose purpose is to keep running descriptive statistics on observations, consisting of one or two Scheme numbers, that are injected into it. It can compute a variety of simple statistics such as the arithmetic mean, the variance, and the standard deviation. It does not record the observations themselves, and therefore cannot compute the median or the mode.

Constructor

(make-tally [ key ])

Returns a newly allocated tally with no observations. The key is an arbitrary Scheme object useful for distinguishing this tally from other tallies; for example, it can be used when tallying observations into multiple bins to record the lower and/or upper limit of each bin. The default value is #f.

Injectors

Some of the statistics may be meaningless if more than one of these injectors is used on any one tally.

(tally! tally value)

Injects value into tally and updatse all descriptive statistics.

(tally-weighted! tally value weight)

Injects value into tally, assigning it a weight of weight (from 0 to 1) for the purpose of calculating weighted sums and weighted averages, and updates all descriptive statistics.

(tally-timed! tally value timestamp)

The same as tally-weighted!, except that the weight is timestamp minus the value of timestamp on the previous call to tally-timed!, or 0 if there was no previous call.

(tally-correlated! tally value1 value2)

Injects value1 into tally, tracking value2 separately for the purpose of calculating correlation and covariance.

Basic statistics

(tally-key tally)

Returns the key of tally.

(tally-count tally)

Returns the number of observations injected so far as an exact integer.

(tally-sum tally)

Returns the sum of all observations injected so far.

(tally-sum tally)

Returns the sum of all observations injected so far.

(tally-product tally)

Returns the product of all observations injected so far.

(tally-harmonic-sum tally)

Returns the harmonic sum of all observations injected so far. This is the sum of the reciprocals of the observation values. If any observation value is zero, returns +nan.0.

(tally-mean tally)

Returns the arithmetic mean of all observations injected so far. This is the quotient of the sum and the count, or +nan.0 if the count is zero.

(tally-geometric-mean tally)

Returns the geometric mean of all observations injected so far. This is the nth root of the product, where n = the count.

(tally-harmonic-mean tally)

Returns the sum of all observations injected so far. This is the count divided by the harmonic sum.

(tally-max tally)

Returns the maximum observation injected so far. If no observations have been injected, returns +inf.0.

(tally-min tally)

Returns the minimum observation injected so far. If no observations have been injected, returns -inf.0.

(tally-range tally)

Returns the difference between the maximum and the minimum. If no observations have been injected, returns +nan.0.

(tally-sample-variance tally)

Returns the sample variance of the observations injected so far. If no observations have been injected, returns +nan.0.

(tally-population-variance tally)

Returns the population variance of the observations injected so far. If no observations have been injected, returns +nan.0.

(tally-sample-standard-deviation tally)

Returns the sample standard deviation of the observations injected so far. If no observations have been injected, returns +nan.0.

(tally-population-standard-deviation tally)

Returns the population standard deviation of the observations injected so far. If no observations have been injected, returns +nan.0.

Weighted and timed statistics

(tally-weighted-sum tally)

Returns the weighted sum of the observations and weights injected so far.

(tally-weighted-mean tally)

Returns the weighted arithmetic mean of the observations and weights injected so far. If no observations have been injected, returns +nan.0.

(tally-timed-sum tally)

Returns the weighted sum of the observations and weights (based on timestamps) injected so far.

(tally-timed-mean tally)

Returns the weighted arithmetic mean of the observations and weights (based on timestamps) injected so far. If no observations have been injected, returns +nan.0.

Covariance and correlation

(tally-sample-covariance tally)

Returns the sample covariance of the pairs of observations injected so far. If no observations have been injected, returns +nan.0.

(tally-population-covariance tally)

Returns the population covariance of the pairs of observations injected so far. If no observations have been injected, returns +nan.0.

(tally-correlation tally)

Returns the correlation based on the pairs of observations injected so far.