criterium.stats — criterium 0.4.6

bca-nonparametric clj

(bca-nonparametric data statistic size alpha rng-factory)

Non-parametric BCa estimate of a statistic on data. Size bootstrap samples are used. Confidence values are returned at the alpha normal quantiles. rng-factory is a method that returns a random number generator to use for the sampling.

An introduction to the bootstrap. Efron, B., & Tibshirani, R. J. (1993).

See http://lib.stat.cmu.edu/S/bootstrap.funs for Efron's original implementation.

bca-nonparametric-eval clj

(bca-nonparametric-eval n size data z-alpha estimate samples jack-samples)

Calculate bootstrap values for given estimate and samples

bca-to-estimate clj

(bca-to-estimate alpha bca-estimate)

bootstrap-estimate clj

(bootstrap-estimate sampled-stat)

Mean, variance and confidence interval. This uses the bootstrapped statistic's variance for the confidence interval, but we should use BCa of ABC.

bootstrap-sample clj

(bootstrap-sample data statistic size rng-factory)

Bootstrap sampling of a statistic, using resampling with replacement.

boxplot-outlier-thresholds clj

(boxplot-outlier-thresholds q1 q3)

Outlier thresholds for given quartiles.

confidence-interval clj

(confidence-interval mean variance)

Find the significance of outliers gicen boostrapped mean and variance estimates. This uses the bootstrapped statistic's variance, but we should use BCa of ABC.

cube clj

(cube x)

Square of argument

drop-at clj

(drop-at n coll)

erf clj

(erf x)

erf polynomial approximation. Maximum error is 1.5e-7. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Milton Abramowitz (Editor), Irene A. Stegun (Editor), 7.1.26

gaussian-weight clj

(gaussian-weight t)

Weight function for gaussian kernel.

jacknife clj

(jacknife data statistic)

Jacknife statistics on data.

kernel-density-estimator clj

(kernel-density-estimator h K n X x)

Kernel density estimator for x, given n samples X, weights K and width h.

mean clj

(mean data)

Arithmetic mean of data.

median clj

(median data)

Calculate the median of a sorted data set References: http://en.wikipedia.org/wiki/Median

modal-estimation-constant clj

(modal-estimation-constant h-k sample-variance)

Kernel function for estimation of multi-modality. h-k is the critical bandwidth, sample-variance is the observed sample variance. Equation 7, Nonparametric assessment of multimodality for univariate data. Salgado-Ugarte IH, Shimizu M

normal-cdf clj

(normal-cdf x)

Probability p(X<x), for a normal distrubtion. Uses the polynomial erf approximation above, and so is not super accurate.

normal-quantile clj

(normal-quantile x)

Normal quantile function. Given a quantile in (0,1), return the normal value for that quantile.

Wichura, MJ. 'Algorithm AS241' The Percentage Points of the Normal Distribution. Applied Statistics, 37, 477-484

polynomial-value clj

(polynomial-value x coefficients)

Evaluate a polynomial at the given value x, for the coefficients given in descending order (so the last element of coefficients is the constant term).

quantile clj

(quantile quantile data)

Calculate the quantile of a sorted data set References: http://en.wikipedia.org/wiki/Quantile

quartiles clj

(quartiles data)

Calculate the quartiles of a sorted data set References: http://en.wikipedia.org/wiki/Quartile

sample clj

(sample x rng)

Sample with replacement.

sample-uniform clj

(sample-uniform n max-val rng)

Provide n samples from a uniform distribution on 0..max-val

scale-bootstrap-estimate clj

(scale-bootstrap-estimate estimate scale)

smoothed-sample clj

(smoothed-sample c-k h-k data deviates)

Smoothed estimation function.

sqr clj

(sqr x)

Square of argument

sum clj

(sum data)

Sum of each data point.

sum-of-squares clj

(sum-of-squares data)

Sum of the squares of each data point.

transpose clj

(transpose data)

Transpose a vector of vectors.

trunc clj

(trunc x)

Round towards zero to an integeral value.

uniform-distribution clj

(uniform-distribution max-val rng)

Return uniformly distributed deviates on 0..max-val use the specified rng.

variance clj

(variance data)

(variance data df)

Sample variance. Returns variance. Ref: Chan et al. Algorithms for computing the sample variance: analysis and recommendations. American Statistician (1983).