fastmath.stats — generateme/fastmath 1.4.0-SNAPSHOT

Statistics functions.

• Descriptive statistics for sequence.
• Correlation / covariance of two sequences.
• Outliers

All functions are backed by Apache Commons Math or SMILE libraries. All work with Clojure sequences.

Descriptive statistics

All in one function stats-map contains:

• :Size - size of the samples, (count ...)
• :Min - minimum value
• :Max - maximum value
• :Range - range of values
• :Mean - mean/average
• :Median - median, see also: median-3
• :Mode - mode, see also: modes
• :Q1 - first quartile, use: percentile, [[quartile]]
• :Q3 - third quartile, use: percentile, [[quartile]]
• :Total - sum of all samples
• :SD - sample standard deviation
• :Variance - variance
• :MAD - median-absolute-deviation
• :SEM - standard error of mean
• :LAV - lower adjacent value, use: adjacent-values
• :UAV - upper adjacent value, use: adjacent-values
• :IQR - interquartile range, (- q3 q1)
• :LOF - lower outer fence, (- q1 (* 3.0 iqr))
• :UOF - upper outer fence, (+ q3 (* 3.0 iqr))
• :LIF - lower inner fence, (- q1 (* 1.5 iqr))
• :UIF - upper inner fence, (+ q3 (* 1.5 iqr))
• :Outliers - list of outliers, samples which are outside outer fences
• :Kurtosis - kurtosis
• :Skewness - skewness
• :SecMoment - second central moment, use: second-moment

Note: percentile and [[quartile]] can have 10 different interpolation strategies. See docs

Correlation / Covariance / Divergence

• covariance
• correlation
• pearson-correlation
• spearman-correlation
• kendall-correlation
• kullback-leibler-divergence
• jensen-shannon-divergence

Other

Normalize samples to have mean=0 and standard deviation = 1 with standardize.

histogram to count samples in evenly spaced ranges.

adjacent-values clj

(adjacent-values vs)

(adjacent-values vs estimation-strategy)

(adjacent-values vs q1 q3)

Lower and upper adjacent values (LAV and UAV).

Let Q1 is 25-percentile and Q3 is 75-percentile. IQR is (- Q3 Q1).

• LAV is smallest value which is greater or equal to the LIF = (- Q1 (* 1.5 IQR)).
• UAV is largest value which is lower or equal to the UIF = (+ Q3 (* 1.5 IQR)).

Optional estimation-strategy argument can be set to change quantile calculations estimation type. See [[estimation-strategies]].

ameasure clj

(ameasure group1 group2)

Vargha-Delaney A measure for two populations a and b

binary-measures clj

(binary-measures truth prediction)

(binary-measures truth prediction true-value false-value)

binary-measures-all clj

(binary-measures-all truth prediction)

(binary-measures-all truth prediction true-value false-value)

https://en.wikipedia.org/wiki/Precision_and_recall

bootstrap clj

(bootstrap vs)

(bootstrap vs samples)

(bootstrap vs samples size)

Generate set of samples of given size from provided data.

Default samples is 50, number of size defaults to 1000

bootstrap-ci clj

(bootstrap-ci vs)

(bootstrap-ci vs alpha)

(bootstrap-ci vs alpha samples)

(bootstrap-ci vs alpha samples stat-fn)

Bootstrap method to calculate confidence interval.

Alpha defaults to 0.98, samples to 1000. Last parameter is statistical function used to measure, default to mean.

ci clj

(ci vs)

(ci vs alpha)

T-student based confidence interval for given data. Alpha value defaults to 0.98.

cliffs-delta clj

(cliffs-delta group1 group2)

Cliff's delta effect size

cohens-d clj

(cohens-d group1 group2)

Cohen's d effect size for two groups

cohens-d-orig clj

(cohens-d-orig group1 group2)

Original version of Cohen's d effect size for two groups

correlation clj

(correlation vs1 vs2)

Correlation of two sequences.

covariance clj

(covariance vs1 vs2)

Covariance of two sequences.

covariance-matrix clj

(covariance-matrix vss)

Generate covariance matrix from seq of seqs. Row order.

estimate-bins clj

(estimate-bins vs)

(estimate-bins vs bins-or-estimate-method)

Estimate number of bins for histogram.

Possible methods are: :sqrt :sturges :rice :doane :scott :freedman-diaconis (default).

estimation-strategies-list clj

extent clj

(extent vs)

Return extent (min, max) values from sequence

glass-delta clj

(glass-delta group1 group2)

Glass's delta effect size for two groups

hedges-g clj

(hedges-g group1 group2)

Hedges's g effect size for two groups

hedges-g* clj

(hedges-g* group1 group2)

Less biased Hedges's g effect size for two groups

histogram clj

(histogram vs)

(histogram vs bins-or-estimate-method)

(histogram vs bins [mn mx])

Calculate histogram.

Returns map with keys:

• :size - number of bins
• :step - distance between bins
• :bins - list of pairs of range lower value and number of hits
• :min - min value
• :max - max value
• :samples - number of used samples

For estimation methods check estimate-bins.

iqr clj

(iqr vs)

(iqr vs estimation-strategy)

Interquartile range.

jensen-shannon-divergence clj

(jensen-shannon-divergence vs1 vs2)

Jensen-Shannon divergence of two sequences.

kendall-correlation clj

(kendall-correlation vs1 vs2)

Kendall's correlation of two sequences.

kullback-leibler-divergence clj

(kullback-leibler-divergence vs1 vs2)

Kullback-Leibler divergence of two sequences.

kurtosis clj

(kurtosis vs)

Calculate kurtosis from sequence.

mad-extent clj

(mad-extent vs__4538__auto__)

median +/- median-absolute-deviation

maximum clj

(maximum vs)

Maximum value from sequence.

mean clj

(mean vs)

Calculate mean of vs

median clj

(median vs)

Calculate median of vs. See median-3.

median-3 clj

(median-3 a b c)

Median of three values. See median.

median-absolute-deviation clj

(median-absolute-deviation vs)

Calculate MAD

minimum clj

(minimum vs)

Minimum value from sequence.

mode clj

(mode vs)

Find the value that appears most often in a dataset vs.

See also modes.

modes clj

(modes vs)

Find the values that appears most often in a dataset vs.

Returns sequence with all most appearing values in increasing order.

See also mode.

outliers clj

(outliers vs)

(outliers vs estimation-strategy)

(outliers vs q1 q3)

Find outliers defined as values outside outer fences.

Let Q1 is 25-percentile and Q3 is 75-percentile. IQR is (- Q3 Q1).

• LIF (Lower Outer Fence) equals (- Q1 (* 1.5 IQR)).
• UIF (Upper Outer Fence) equals (+ Q3 (* 1.5 IQR)).

Returns sequence.

Optional estimation-strategy argument can be set to change quantile calculations estimation type. See [[estimation-strategies]].

pearson-correlation clj

(pearson-correlation vs1 vs2)

Pearson's correlation of two sequences.

percentile clj

(percentile vs p)

(percentile vs p estimation-strategy)

Calculate percentile of a vs.

Percentile p is from range 0-100.

See docs.

Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

See also quantile.

percentile-extent clj

(percentile-extent vs)

(percentile-extent vs p)

(percentile-extent vs p1 p2)

(percentile-extent vs p1 p2 estimation-strategy)

Return percentile range.

percentiles clj

(percentiles vs ps)

(percentiles vs ps estimation-strategy)

Calculate percentiles of a vs.

Percentiles are sequence of values from range 0-100.

See docs.

Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

See also quantile.

population-stddev clj

(population-stddev vs)

(population-stddev vs u)

Calculate population standard deviation of vs.

See stddev.

population-variance clj

(population-variance vs)

(population-variance vs u)

Calculate population variance of vs.

See variance.

quantile clj

(quantile vs q)

(quantile vs q estimation-strategy)

Calculate quantile of a vs.

Quantile q is from range 0.0-1.0.

See docs for interpolation strategy.

Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

See also percentile.

quantiles clj

(quantiles vs qs)

(quantiles vs qs estimation-strategy)

Calculate quantiles of a vs.

Quantilizes is sequence with values from range 0.0-1.0.

See docs for interpolation strategy.

Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

See also percentiles.

second-moment clj

(second-moment vs)

Calculate second moment from sequence.

It's a sum of squared deviations from the sample mean

sem clj

(sem vs)

Standard error of mean

sem-extent clj

(sem-extent vs__4538__auto__)

mean +/- sem

skewness clj

(skewness vs)

Calculate kurtosis from sequence.

spearman-correlation clj

(spearman-correlation vs1 vs2)

Spearman's correlation of two sequences.

standardize clj

(standardize vs)

Normalize samples to have mean = 0 and stddev = 1.

stats-map clj

(stats-map vs)

(stats-map vs estimation-strategy)

Calculate several statistics of vs and return as map.

Optional estimation-strategy argument can be set to change quantile calculations estimation type. See [[estimation-strategies]].

stddev clj

(stddev vs)

(stddev vs u)

Calculate standard deviation of vs.

See population-stddev.

stddev-extent clj

(stddev-extent vs__4538__auto__)

mean +/- stddev

sum clj

(sum vs)

Sum of all vs values.

ttest-one-sample clj

(ttest-one-sample xs)

(ttest-one-sample xs
                  {:keys [alpha sides mu]
                   :or {alpha 0.05 sides :two-sided mu 0.0}})

ttest-two-samples clj

(ttest-two-samples
  xs
  ys
  {:keys [alpha sides mu paired? equal-variances?]
   :or {alpha 0.05 sides :two-sided mu 0.0 paired? false equal-variances? false}
   :as params})

variance clj

(variance vs)

(variance vs u)

Calculate variance of vs.

See population-variance.