library.stat Submodule

Module Summary

Interfaces for the NAG Mark 30.3 stat Chapter.

stat - Simple Calculations on Statistical Data

This module covers the following topics:

descriptive statistics and exploratory data analysis;

statistical distribution functions and their inverses;

testing for Normality and other distributions.

See Also

naginterfaces.library.examples.stat :

This subpackage contains examples for the stat module. See also the Examples subsection.

Functionality Index

Descriptive statistics / Exploratory analysis

summaries

frequency / contingency table

one variable: frequency_table()

two variables, with ${\chi }^2$ and Fisher’s exact test: contingency_table()

mean, variance, skewness, kurtosis (one variable)

combine summaries: summary_onevar_combine()

from frequency table: summary_freq()

from raw data: summary_onevar()

mean, variance, sums of squares and products (two variables): summary_2var()

median, hinges / quartiles, minimum, maximum: five_point_summary()

quantiles

approximate

large data stream of fixed size: quantiles_stream_fixed()

large data stream of unknown size: quantiles_stream_arbitrary()

unordered vector

unweighted: quantiles()

rolling window

mean, standard deviation (one variable): moving_average()

Distributions

${\chi }^2$

vectorized deviates: inv_cdf_chisq_vector()

vectorized probabilities: prob_chisq_vector()

Beta

central

deviates

scalar: inv_cdf_beta()

vectorized: inv_cdf_beta_vector()

probabilities and probability density function

scalar: prob_beta()

vectorized: prob_beta_vector()

non-central

probabilities: prob_beta_noncentral()

binomial

distribution function

scalar: prob_binomial()

vectorized: prob_binomial_vector()

Dickey–Fuller unit root test

probabilities: prob_dickey_fuller_unit()

Durbin–Watson statistic

probabilities: prob_durbin_watson()

energy loss distributions

Landau

density: pdf_landau()

derivative of density: pdf_landau_deriv()

distribution: prob_landau()

first moment: pdf_landau_moment1()

inverse distribution: inv_cdf_landau()

second moment: pdf_landau_moment2()

Vavilov

density: pdf_vavilov()

distribution: prob_vavilov()

initialization: init_vavilov()

$F$

central

deviates

scalar: inv_cdf_f()

vectorized: inv_cdf_f_vector()

probabilities

scalar: prob_f()

vectorized: prob_f_vector()

non-central

probabilities: prob_f_noncentral()

gamma

deviates

scalar: inv_cdf_gamma()

vectorized: inv_cdf_gamma_vector()

probabilities

scalar: prob_gamma()

vectorized: prob_gamma_vector()

probability density function

scalar: pdf_gamma()

vectorized: pdf_gamma_vector()

Hypergeometric

distribution function

scalar: prob_hypergeom()

vectorized: prob_hypergeom_vector()

Kolomogorov–Smirnov

probabilities

one-sample: prob_kolmogorov1()

two-sample: prob_kolmogorov2()

Normal

bivariate

probabilities: prob_bivariate_normal()

multivariate

probabilities: prob_multi_normal()

probability density function

vectorized: pdf_multi_normal_vector()

quadratic forms

cumulants and moments: moments_quad_form()

moments of ratios: moments_ratio_quad_forms()

univariate

deviates

scalar: inv_cdf_normal()

vectorized: inv_cdf_normal_vector()

probabilities

scalar: prob_normal()

vectorized: prob_normal_vector()

probability density function

scalar: pdf_normal()

vectorized: pdf_normal_vector()

reciprocal of Mill’s Ratio: mills_ratio()

Shapiro and Wilk’s test for Normality: test_shapiro_wilk()

Poisson

distribution function

scalar: prob_poisson()

vectorized: prob_poisson_vector()

Student’s $t$

central

bivariate

probabilities: prob_bivariate_students_t()

multivariate

probabilities: prob_multi_students_t()

univariate

deviates

scalar: inv_cdf_students_t()

vectorized: inv_cdf_students_t_vector()

probabilities

scalar: prob_students_t()

vectorized: prob_students_t_vector()

non-central

probabilities: prob_students_t_noncentral()

Studentized range statistic

deviates: inv_cdf_studentized_range()

probabilities: prob_studentized_range()

von Mises

probabilities: prob_vonmises()

${\chi }^2$

central

deviates: inv_cdf_chisq()

probabilities: prob_chisq()

probability of linear combination: prob_chisq_lincomb()

non-central

probabilities: prob_chisq_noncentral()

probability of linear combination: prob_chisq_noncentral_lincomb()

Scores

Normal scores

accurate: normal_scores_exact()

approximate: normal_scores_approx()

variance-covariance matrix: normal_scores_var()

Normal scores, ranks or exponential (Savage) scores: ranks_and_scores()

For full information please refer to the NAG Library document

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g01/g01intro.html

Examples

naginterfaces.library.examples.stat.moving_average_ex.main()

Example for naginterfaces.library.stat.moving_average().

Calculate the mean and, optionally, the standard deviation using a rolling window for an arbitrary sized data stream.

>>> main()
naginterfaces.library.stat.moving_average Python Example Results.
Spencer's 15-point moving average for the change in rate of the
Earth's rotation between 1821 and 1850.
Interval         Mean        Std. Dev.
--------------------------------------
[  1, 15]       -427.6           -
[  2, 16]       -332.5           -
[  3, 17]       -337.1           -
[  4, 18]       -438.2           -
[  5, 19]       -604.4           -
[  6, 20]       -789.4           -
[  7, 21]       -935.4           -
[  8, 22]       -990.6           -
[  9, 23]       -927.1           -
[ 10, 24]       -752.1           -
[ 11, 25]       -501.3           -
[ 12, 26]       -227.2           -
[ 13, 27]         23.2           -
[ 14, 28]        236.2           -
[ 15, 29]        422.4           -
[ 16, 30]        604.2           -
Total number of observations: 30
Length of window: 15