kixi.stats.core — kixi/stats 0.5.3

adjusted-r-squared clj/s

(adjusted-r-squared fy-hat fy k)

Given two functions: (fŷ input) and (fy input), returning the predicted and actual values of y respectively, and a constant k equal to the number of terms in the model, estimates the adjusted coefficient of determination R^2 using Wherry's Formula-1. This is the fraction of variance in y explained by the model, adjusted for the number of terms in the model. https://stats.stackexchange.com/questions/48703/what-is-the-adjusted-r-squared-formula-in-lm-in-r-and-how-should-it-be-interpret

arithmetic-mean clj/s

Calculates the arithmetic mean of numeric inputs.

chi-squared-test clj/s

(chi-squared-test & fxs)

Given a sequence of functions, each of which returns the categorical value (e.g. keyword or string) of a factor, performs a X^2 test of independence.

correlation clj/s

(correlation fx fy)

Given two functions: (fx input) and (fy input), each of which returns a number, estimates the unbiased linear correlation coefficient between fx and fy over inputs. Ignores any records where fx or fy are nil. If there are no records with values for fx and fy, the correlation is nil. See http://mathworld.wolfram.com/CorrelationCoefficient.html.

correlation-matrix clj/s

(correlation-matrix kvs)

Given a map of key names to functions that extract values for those keys from an input, computes the correlation for each of the n^2 key pairs. For example:

(correlation-matrix {:name-length #(.length (:name %))
                     :age         :age
                     :num-cats    (comp count :cats)})

will, when reduced, return a map like:

{[:name-length :age]      0.56
 [:name-length :num-cats] 0.95
 ...}

count clj/s

Calculates the count of inputs.

covariance clj/s

Alias for covariance-s

covariance-matrix clj/s

(covariance-matrix kvs)

Given a map of key names to functions that extract values for those keys from an input, computes the covariance for each of the n^2 key pairs. For example:

(covariance-matrix {:name-length #(.length (:name %))
                    :age         :age
                    :num-cats    (comp count :cats)})

will, when reduced, return a map like:

{[:name-length :age]      0.56
 [:name-length :num-cats] 0.95
 ...}

covariance-p clj/s

(covariance-p fx fy)

Given two functions of an input (fx input) and (fy input), each of which returns a number, estimates the population covariance of those functions over inputs.

Ignores any inputs where (fx input) or (fy input) are nil. If no inputs have both x and y, returns nil.

covariance-s clj/s

(covariance-s fx fy)

Given two functions of an input (fx input) and (fy input), each of which returns a number, estimates the unbiased covariance of those functions over inputs.

Ignores any inputs where (fx input) or (fy input) are nil. If no inputs have both x and y, returns nil.

cramers-v clj/s

(cramers-v fx fy)

Cramer's Phi is the intercorrelation of two discrete variables and may be used with variables having two or more levels. It gives a value between 0 and +1 (inclusive). Given two functions: (fx input) and (fy input), each of which returns a the relevant discrete value.

cross-tabulate clj/s

(cross-tabulate & fxs)

Given a sequence of n functions, each of which returns a categorical value (e.g. keyword or string) of a factor, calculates an n-dimensional contingency table implementing PContingencyTable. This can be passed to kixi.stats.test/chi-squared-test to determine if the relationship between factors is significant. See also: kixi.stats.core/chi-squared-test

geometric-mean clj/s

Calculates the geometric mean of numeric inputs. Defined only for positive numbers.

harmonic-mean clj/s

Calculates the harmonic mean of numeric inputs.

histogram clj

Calculates a histogram of numeric inputs using the t-digest with default arguments.

iqr clj

Calculates the interquartile range of numeric inputs.

kurtosis clj/s

Alias for kurtosis-s.

kurtosis-p clj/s

Calculates the population kurtosis of numeric inputs. See http://www.macroption.com/kurtosis-formula/

kurtosis-s clj/s

Estimates the sample kurtosis of numeric inputs. See https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance and http://www.real-statistics.com/descriptive-statistics/symmetry-skewness-kurtosis.

max clj/s

Like clojure.core/max, but transducer and nil-friendly.

mean clj/s

Alias for arithmetic-mean.

median clj

Calculates the median of numeric inputs.

min clj/s

Like clojure.core/min, but transducer and nil-friendly.

monoid clj/s

(monoid f init)

Add 0-arity returning init to f.

mse clj/s

(mse fy-hat fy)

Given two functions: (fŷ input) and (fy input), returning the predicted and actual values of y respectively, calculates the mean squared error of the estimate.

proportion clj/s

(proportion pred)

Calculate the proportion of inputs for which pred returns true.

r-squared clj/s

(r-squared fy-hat fy)

Given two functions: (fŷ input) and (fy input), returning the predicted and actual values of y respectively, estimates the coefficient of determination R^2. This is the fraction of variance in y explained by the model.

regression-confidence-interval clj/s

(regression-confidence-interval fx fy)

(regression-confidence-interval fx fy alpha)

(regression-confidence-interval fx fy alpha x)

Given two functions: (fx input) and (fy input), each of which returns a number, and an x value, calculates the standard error of the least squares linear model of fx and fy over inputs. Ignores any records with fx or fy are nil. If there are no records with values for fx and fy, the standard error of the estimate is nil.

regression-prediction-confidence-interval clj/s

(regression-prediction-confidence-interval fx fy)

(regression-prediction-confidence-interval fx fy alpha)

(regression-prediction-confidence-interval fx fy alpha x)

Given two functions: (fx input) and (fy input), each of which returns a number, and an x value, calculates the standard error of the least squares linear model of fx and fy over inputs. Ignores any records with fx or fy are nil. If there are no records with values for fx and fy, the standard error of the estimate is nil.

regression-prediction-standard-error clj/s

(regression-prediction-standard-error fx fy)

(regression-prediction-standard-error fx fy x)

Given two functions: (fx input) and (fy input), each of which returns a number, and an x value, calculates the standard error of the least squares linear model of fx and fy over inputs. Ignores any records with fx or fy are nil. If there are no records with values for fx and fy, the standard error of the estimate is nil.

regression-standard-error clj/s

(regression-standard-error fx fy)

(regression-standard-error fx fy x)

Given two functions: (fx input) and (fy input), each of which returns a number, and an x value, calculates the standard error of the least squares linear model of fx and fy over inputs. Ignores any records with fx or fy are nil. If there are no records with values for fx and fy, the standard error of the estimate is nil.

rmse clj/s

(rmse fy-hat fy)

Given two functions: (fŷ input) and (fy input), returning the predicted and actual values of y respectively, calculates the root mean squared error of the estimate.

share clj/s

Alias for proportion

simple-linear-regression clj/s

(simple-linear-regression fx fy)

Given two functions: (fx input) and (fy input), each of which returns a number, calculates a least squares linear model between fx and fy over inputs. Returns a vector containing the coefficients: offset and slope. Ignores any records with fx or fy are nil. If there are no records with values for fx and fy, the linear relationship is nil. See https://en.wikipedia.org/wiki/Simple_linear_regression.

simple-t-test clj/s

(simple-t-test {:keys [mu sd]})

Performs a simple t test against a specified population mean and standard deviation. The standard deviation is optional, if not provided, a 'plug-in' test using the sample's sd will be performed instead. mu: the population mean sd: (optional) the population standard deviation

simple-z-test clj/s

(simple-z-test {:keys [mu sd]})

Performs a simple z test against a specified population mean and standard deviation. The standard deviation is optional, if not provided, a 'plug-in' test using the sample's sd will be performed instead. mu: the population mean sd: (optional) the population standard deviation

skewness clj/s

Alias for skewness-s.

skewness-p clj/s

Calculates the population skewness of numeric inputs. See: http://www.real-statistics.com/descriptive-statistics/symmetry-skewness-kurtosis.

skewness-s clj/s

Estimates the sample skewness of numeric inputs. See https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.

standard-deviation clj/s

Alias for standard-deviation-s.

standard-deviation-p clj/s

Calculates the population standard deviation of numeric inputs.

standard-deviation-s clj/s

Estimates the sample standard deviation of numeric inputs.

standard-error clj/s

Alias for standard-error-s

standard-error-s clj/s

Calculates the standard error of sample means.

sum-squares clj/s

summary clj

Calculates the five number summary of numeric inputs.

t-test clj/s

(t-test fx fy)

Given two functions of an input (fx input) and (fy input), each of which returns a number, performs the t test of mean significance of those functions over inputs. Ignores only inputs where both (fx input) and (fy input) are nil.

variance clj/s

Alias for variance-s.

variance-p clj/s

Calculates the population variance of numeric inputs.

variance-s clj/s

Estimates an unbiased variance of numeric inputs.

z-test clj/s

(z-test fx fy)

Given two functions of an input (fx input) and (fy input), each of which returns a number, performs the z-test of mean significance of those functions over inputs.

Ignores only inputs where both (fx input) and (fy input) are nil.