# NAG FL InterfaceG01 (Stat)Simple Calculations on Statistical Data

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G01 (Stat) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
g01abf 4 nagf_stat_summary_2var
Means, corrected sums of squares and cross-products, etc., two variables, from raw data
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
g01aef 4 nagf_stat_frequency_table
Frequency table from raw data
g01aff 4 nagf_stat_contingency_table
Two-way contingency table analysis, with ${\chi }^{2}$/Fisher's exact test
g01alf 14 nagf_stat_five_point_summary
Computes a five-point summary (median, hinges and extremes)
g01amf 22 nagf_stat_quantiles
Find quantiles of an unordered vector, real numbers
g01anf 23 nagf_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
g01apf 23 nagf_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
g01arf 14 nagf_stat_plot_stem_leaf
Constructs a stem and leaf plot
g01asf 14 nagf_stat_plot_box_whisker
Constructs a box and whisker plot
g01atf 24 nagf_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
g01auf 24 nagf_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after g01atf
g01bjf 13 nagf_stat_prob_binomial
Binomial distribution function
g01bkf 13 nagf_stat_prob_poisson
Poisson distribution function
g01blf 13 nagf_stat_prob_hypergeom
Hypergeometric distribution function
g01daf 8 nagf_stat_normal_scores_exact
Normal scores, accurate values
g01dbf 12 nagf_stat_normal_scores_approx
Normal scores, approximate values
g01dcf 12 nagf_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
g01ddf 12 nagf_stat_test_shapiro_wilk
Shapiro and Wilk's $W$ test for Normality
g01dhf 15 nagf_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
g01eaf 15 nagf_stat_prob_normal
Computes probabilities for the standard Normal distribution
g01ebf 14 nagf_stat_prob_students_t
Computes probabilities for Student's $t$-distribution
g01ecf 14 nagf_stat_prob_chisq
Computes probabilities for ${\chi }^{2}$ distribution
g01edf 14 nagf_stat_prob_f
Computes probabilities for $F$-distribution
g01eef 14 nagf_stat_prob_beta
Computes upper and lower tail probabilities and probability density function for the beta distribution
g01eff 14 nagf_stat_prob_gamma
Computes probabilities for the gamma distribution
g01emf 15 nagf_stat_prob_studentized_range
Computes probability for the Studentized range statistic
g01epf 15 nagf_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
g01erf 16 nagf_stat_prob_vonmises
Computes probability for von Mises distribution
g01etf 21 nagf_stat_prob_landau
Landau distribution function
g01euf 21 nagf_stat_prob_vavilov
Vavilov distribution function
g01ewf 25 nagf_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
g01eyf 14 nagf_stat_prob_kolmogorov1
Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
g01ezf 14 nagf_stat_prob_kolmogorov2
Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
g01faf 15 nagf_stat_inv_cdf_normal
Computes deviates for the standard Normal distribution
g01fbf 14 nagf_stat_inv_cdf_students_t
Computes deviates for Student's $t$-distribution
g01fcf 14 nagf_stat_inv_cdf_chisq
Computes deviates for the ${\chi }^{2}$ distribution
g01fdf 14 nagf_stat_inv_cdf_f
Computes deviates for the $F$-distribution
g01fef 14 nagf_stat_inv_cdf_beta
Computes deviates for the beta distribution
g01fff 14 nagf_stat_inv_cdf_gamma
Computes deviates for the gamma distribution
g01fmf 15 nagf_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
g01ftf 21 nagf_stat_inv_cdf_landau
Landau inverse function $\Psi \left(x\right)$
g01gbf 14 nagf_stat_prob_students_t_noncentral
Computes probabilities for the non-central Student's $t$-distribution
g01gcf 14 nagf_stat_prob_chisq_noncentral
Computes probabilities for the non-central ${\chi }^{2}$ distribution
g01gdf 14 nagf_stat_prob_f_noncentral
Computes probabilities for the non-central $F$-distribution
g01gef 14 nagf_stat_prob_beta_noncentral
Computes probabilities for the non-central beta distribution
g01haf 14 nagf_stat_prob_bivariate_normal
Computes probability for the bivariate Normal distribution
g01hbf 15 nagf_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
g01hcf 23 nagf_stat_prob_bivariate_students_t
Computes probabilities for the bivariate Student's $t$-distribution
g01hdf 24 nagf_stat_prob_multi_students_t
Computes the probability for the multivariate Student's $t$-distribution
g01jcf 14 nagf_stat_prob_chisq_noncentral_lincomb
Computes probability for a positive linear combination of ${\chi }^{2}$ variables
g01jdf 15 nagf_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) ${\chi }^{2}$ variables
g01kaf 23 nagf_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
g01kff 23 nagf_stat_pdf_gamma
Calculates the value for the probability density function of the gamma distribution at a chosen point
g01kkf 24 nagf_stat_pdf_gamma_vector
Computes a vector of values for the probability density function of the gamma distribution
g01kqf 24 nagf_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
g01lbf 24 nagf_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
g01mbf 15 nagf_stat_mills_ratio
Computes reciprocal of Mills' Ratio
g01mtf 21 nagf_stat_pdf_landau
Landau density function $\varphi \left(\lambda \right)$
g01muf 21 nagf_stat_pdf_vavilov
Vavilov density function ${\varphi }_{V}\left(\lambda ;\kappa ,{\beta }^{2}\right)$
Cumulants and moments of quadratic forms in Normal variables
Moments of ratios of quadratic forms in Normal variables, and related statistics
g01ptf 21 nagf_stat_pdf_landau_moment1
Landau first moment function ${\Phi }_{1}\left(x\right)$
g01qtf 21 nagf_stat_pdf_landau_moment2
Landau second moment function ${\Phi }_{2}\left(x\right)$
g01rtf 21 nagf_stat_pdf_landau_deriv
Landau derivative function ${\varphi }^{\prime }\left(\lambda \right)$
g01saf 24 nagf_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
g01sbf 24 nagf_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's $t$-distribution
g01scf 24 nagf_stat_prob_chisq_vector
Computes a vector of probabilities for ${\chi }^{2}$ distribution
g01sdf 24 nagf_stat_prob_f_vector
Computes a vector of probabilities for $F$-distribution
g01sef 24 nagf_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
g01sff 24 nagf_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
g01sjf 24 nagf_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
g01skf 24 nagf_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
g01slf 24 nagf_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
g01taf 24 nagf_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
g01tbf 24 nagf_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's $t$-distribution
g01tcf 24 nagf_stat_inv_cdf_chisq_vector
Computes a vector of deviates for ${\chi }^{2}$ distribution
g01tdf 24 nagf_stat_inv_cdf_f_vector
Computes a vector of deviates for $F$-distribution
g01tef 24 nagf_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
g01tff 24 nagf_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
g01waf 24 nagf_stat_moving_average
Computes the mean and standard deviation using a rolling window
g01zuf 21 nagf_stat_init_vavilov
Initialization routine for g01muf and g01euf