# NAG CL 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.

Function
Mark of
Introduction

Purpose
Mean, variance, skewness, kurtosis, etc., one variable, from frequency table
g01aec 6 nag_stat_frequency_table
Frequency table from raw data
g01alc 4 nag_stat_five_point_summary
Five-point summary (median, hinges and extremes)
g01amc 9 nag_stat_quantiles
Quantiles of a set of unordered values
g01anc 23 nag_stat_quantiles_stream_fixed
Calculates approximate quantiles from a data stream of known size
g01apc 23 nag_stat_quantiles_stream_arbitrary
Calculates approximate quantiles from a data stream of unknown size
g01atc 24 nag_stat_summary_onevar
Computes univariate summary information: mean, variance, skewness, kurtosis
g01auc 24 nag_stat_summary_onevar_combine
Combines multiple sets of summary information, for use after g01atc
g01bjc 4 nag_stat_prob_binomial
Binomial distribution function
g01bkc 4 nag_stat_prob_poisson
Poisson distribution function
g01blc 4 nag_stat_prob_hypergeom
Hypergeometric distribution function
g01dac 7 nag_stat_normal_scores_exact
Normal scores, accurate values
g01dcc 7 nag_stat_normal_scores_var
Normal scores, approximate variance-covariance matrix
g01ddc 4 nag_stat_test_shapiro_wilk
Shapiro and Wilk's $W$ test for Normality
g01dhc 4 nag_stat_ranks_and_scores
Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores
g01eac 4 nag_stat_prob_normal
Probabilities for the standard Normal distribution
g01ebc 1 nag_stat_prob_students_t
Probabilities for Student's $t$-distribution
g01ecc 1 nag_stat_prob_chisq
Probabilities for ${\chi }^{2}$ distribution
g01edc 1 nag_stat_prob_f
Probabilities for $F$-distribution
g01eec 1 nag_stat_prob_beta
Upper and lower tail probabilities and probability density function for the beta distribution
g01efc 1 nag_stat_prob_gamma
Probabilities for the gamma distribution
g01emc 7 nag_stat_prob_studentized_range
Computes probability for the Studentized range statistic
g01epc 7 nag_stat_prob_durbin_watson
Computes bounds for the significance of a Durbin–Watson statistic
g01erc 7 nag_stat_prob_vonmises
Computes probability for von Mises distribution
g01etc 7 nag_stat_prob_landau
Landau distribution function
g01euc 7 nag_stat_prob_vavilov
Vavilov distribution function
g01ewc 25 nag_stat_prob_dickey_fuller_unit
Computes probabilities for the Dickey–Fuller unit root test
g01eyc 7 nag_stat_prob_kolmogorov1
Computes probabilities for the one-sample Kolmogorov–Smirnov distribution
g01ezc 7 nag_stat_prob_kolmogorov2
Computes probabilities for the two-sample Kolmogorov–Smirnov distribution
g01fac 4 nag_stat_inv_cdf_normal
Deviates for the Normal distribution
g01fbc 1 nag_stat_inv_cdf_students_t
Deviates for Student's $t$-distribution
g01fcc 1 nag_stat_inv_cdf_chisq
Deviates for the ${\chi }^{2}$ distribution
g01fdc 1 nag_stat_inv_cdf_f
Deviates for the $F$-distribution
g01fec 1 nag_stat_inv_cdf_beta
Deviates for the beta distribution
g01ffc 1 nag_stat_inv_cdf_gamma
Deviates for the gamma distribution
g01fmc 7 nag_stat_inv_cdf_studentized_range
Computes deviates for the Studentized range statistic
g01ftc 7 nag_stat_inv_cdf_landau
Landau inverse function $\Psi \left(x\right)$
g01gbc 6 nag_stat_prob_students_t_noncentral
Computes probabilities for the non-central Student's $t$-distribution
g01gcc 6 nag_stat_prob_chisq_noncentral
Computes probabilities for the non-central ${\chi }^{2}$ distribution
g01gdc 6 nag_stat_prob_f_noncentral
Computes probabilities for the non-central $F$-distribution
g01gec 6 nag_stat_prob_beta_noncentral
Computes probabilities for the non-central beta distribution
g01hac 1 nag_stat_prob_bivariate_normal
Probability for the bivariate Normal distribution
g01hbc 6 nag_stat_prob_multi_normal
Computes probabilities for the multivariate Normal distribution
g01hcc 23 nag_stat_prob_bivariate_students_t
Computes probabilities for the bivariate Student's $t$-distribution
g01hdc 24 nag_stat_prob_multi_students_t
Computes the probability for the multivariate Student's $t$-distribution
g01jcc 7 nag_stat_prob_chisq_noncentral_lincomb
Computes probability for a positive linear combination of ${\chi }^{2}$ variables
g01jdc 7 nag_stat_prob_chisq_lincomb
Computes lower tail probability for a linear combination of (central) ${\chi }^{2}$ variables
g01kac 9 nag_stat_pdf_normal
Calculates the value for the probability density function of the Normal distribution at a chosen point
g01kfc 9 nag_stat_pdf_gamma
Calculates the value for the probability density function of the gamma distribution at a chosen point
g01kkc 23 nag_stat_pdf_gamma_vector
Computes a vector of values for the probability density function of the gamma distribution
g01kqc 23 nag_stat_pdf_normal_vector
Computes a vector of values for the probability density function of the Normal distribution
g01lbc 24 nag_stat_pdf_multi_normal_vector
Computes a vector of values for the probability density function of the multivariate Normal distribution
g01mbc 7 nag_stat_mills_ratio
Computes reciprocal of Mills' Ratio
g01mtc 7 nag_stat_pdf_landau
Landau density function $\varphi \left(\lambda \right)$
g01muc 7 nag_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
g01ptc 7 nag_stat_pdf_landau_moment1
Landau first moment function ${\Phi }_{1}\left(x\right)$
g01qtc 7 nag_stat_pdf_landau_moment2
Landau second moment function ${\Phi }_{2}\left(x\right)$
g01rtc 7 nag_stat_pdf_landau_deriv
Landau derivative function ${\varphi }^{\prime }\left(\lambda \right)$
g01sac 23 nag_stat_prob_normal_vector
Computes a vector of probabilities for the standard Normal distribution
g01sbc 23 nag_stat_prob_students_t_vector
Computes a vector of probabilities for the Student's $t$-distribution
g01scc 23 nag_stat_prob_chisq_vector
Computes a vector of probabilities for ${\chi }^{2}$ distribution
g01sdc 23 nag_stat_prob_f_vector
Computes a vector of probabilities for $F$-distribution
g01sec 23 nag_stat_prob_beta_vector
Computes a vector of probabilities for the beta distribution
g01sfc 23 nag_stat_prob_gamma_vector
Computes a vector of probabilities for the gamma distribution
g01sjc 23 nag_stat_prob_binomial_vector
Computes a vector of probabilities for the binomial distribution
g01skc 23 nag_stat_prob_poisson_vector
Computes a vector of probabilities for the Poisson distribution
g01slc 23 nag_stat_prob_hypergeom_vector
Computes a vector of probabilities for the hypergeometric distribution
g01tac 23 nag_stat_inv_cdf_normal_vector
Computes a vector of deviates for the standard Normal distribution
g01tbc 23 nag_stat_inv_cdf_students_t_vector
Computes a vector of deviates for Student's $t$-distribution
g01tcc 23 nag_stat_inv_cdf_chisq_vector
Computes a vector of deviates for ${\chi }^{2}$ distribution
g01tdc 23 nag_stat_inv_cdf_f_vector
Computes a vector of deviates for $F$-distribution
g01tec 23 nag_stat_inv_cdf_beta_vector
Computes a vector of deviates for the beta distribution
g01tfc 23 nag_stat_inv_cdf_gamma_vector
Computes a vector of deviates for the gamma distribution
g01wac 24 nag_stat_moving_average
Computes the mean and standard deviation using a rolling window
g01zuc 7 nag_stat_init_vavilov
Initialization function for g01muc and g01euc