# NAG Library Chapter Contents

## G01 (stat)Simple Calculations on Statistical Data

G01 (stat) Chapter Introduction – a description of the Chapter and an overview of the algorithms available

 RoutineName Mark ofIntroduction Purpose g01abf Example Text Example Data 4 nagf_stat_summary_2var Means, corrected sums of squares and cross-products, etc., two variables, from raw data g01adf Example Text Example Data 4 nagf_stat_summary_freq Mean, variance, skewness, kurtosis, etc., one variable, from frequency table g01aef Example Text Example Data 4 nagf_stat_frequency_table Frequency table from raw data g01aff Example Text Example Data 4 nagf_stat_contingency_table Two-way contingency table analysis, with ${\chi }^{2}$/Fisher's exact test g01agf Example Text Example Data 8 nagf_stat_withdraw_plot_scatter_2var Lineprinter scatterplot of two variablesNote: this routine is scheduled for withdrawal at Mark 27, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. g01ahf Example Text Example Data 8 nagf_stat_withdraw_plot_scatter_normal Lineprinter scatterplot of one variable against Normal scoresNote: this routine is scheduled for withdrawal at Mark 27, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. g01ajf Example Text Example Data 10 nagf_stat_withdraw_plot_histogram Lineprinter histogram of one variableNote: this routine is scheduled for withdrawal at Mark 27, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. g01alf Example Text Example Data 14 nagf_stat_5pt_summary Computes a five-point summary (median, hinges and extremes) g01amf Example Text Example Data 22 nagf_stat_quantiles Find quantiles of an unordered vector, real numbers g01anf Example Text Example Data 23 nagf_stat_quantiles_stream_fixed Calculates approximate quantiles from a data stream of known size g01apf Example Text Example Data 23 nagf_stat_quantiles_stream_arbitrary Calculates approximate quantiles from a data stream of unknown size g01arf Example Text Example Data 14 nagf_stat_plot_stem_leaf Constructs a stem and leaf plot g01asf Example Text Example Data 14 nagf_stat_plot_box_whisker Constructs a box and whisker plot g01atf Example Text Example Data 24 nagf_stat_summary_onevar Computes univariate summary information: mean, variance, skewness, kurtosis g01auf Example Text Example Data 24 nagf_stat_summary_onevar_combine Combines multiple sets of summary information, for use after g01atf g01bjf Example Text Example Data 13 nagf_stat_prob_binomial Binomial distribution function g01bkf Example Text Example Data 13 nagf_stat_prob_poisson Poisson distribution function g01blf Example Text Example Data 13 nagf_stat_prob_hypergeom Hypergeometric distribution function g01daf Example TextExample Plot 8 nagf_stat_normal_scores_exact Normal scores, accurate values g01dbf Example TextExample Plot 12 nagf_stat_normal_scores_approx Normal scores, approximate values g01dcf Example Text 12 nagf_stat_normal_scores_var Normal scores, approximate variance-covariance matrix g01ddf Example Text Example Data 12 nagf_stat_test_shapiro_wilk Shapiro and Wilk's $W$ test for Normality g01dhf Example Text Example Data 15 nagf_stat_ranks_and_scores Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores g01eaf Example Text Example Data 15 nagf_stat_prob_normal Computes probabilities for the standard Normal distribution g01ebf Example Text Example Data 14 nagf_stat_prob_students_t Computes probabilities for Student's $t$-distribution g01ecf Example Text Example Data 14 nagf_stat_prob_chisq Computes probabilities for ${\chi }^{2}$ distribution g01edf Example Text Example Data 14 nagf_stat_prob_f Computes probabilities for $F$-distribution g01eef Example Text Example Data 14 nagf_stat_prob_beta Computes upper and lower tail probabilities and probability density function for the beta distribution g01eff Example Text Example Data 14 nagf_stat_prob_gamma Computes probabilities for the gamma distribution g01emf Example Text Example Data 15 nagf_stat_prob_studentized_range Computes probability for the Studentized range statistic g01epf Example Text Example Data 15 nagf_stat_prob_durbin_watson Computes bounds for the significance of a Durbin–Watson statistic g01erf Example Text Example Data 16 nagf_stat_prob_vonmises Computes probability for von Mises distribution g01etf Example Text Example Data 21 nagf_stat_prob_landau Landau distribution function g01euf Example Text Example Data 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 Example Text Example Data 14 nagf_stat_prob_kolmogorov1 Computes probabilities for the one-sample Kolmogorov–Smirnov distribution g01ezf Example Text Example Data 14 nagf_stat_prob_kolmogorov2 Computes probabilities for the two-sample Kolmogorov–Smirnov distribution g01faf Example Text Example Data 15 nagf_stat_inv_cdf_normal Computes deviates for the standard Normal distribution g01fbf Example Text Example Data 14 nagf_stat_inv_cdf_students_t Computes deviates for Student's $t$-distribution g01fcf Example Text Example Data 14 nagf_stat_inv_cdf_chisq Computes deviates for the ${\chi }^{2}$ distribution g01fdf Example Text Example Data 14 nagf_stat_inv_cdf_f Computes deviates for the $F$-distribution g01fef Example Text Example Data 14 nagf_stat_inv_cdf_beta Computes deviates for the beta distribution g01fff Example Text Example Data 14 nagf_stat_inv_cdf_gamma Computes deviates for the gamma distribution g01fmf Example Text Example Data 15 nagf_stat_inv_cdf_studentized_range Computes deviates for the Studentized range statistic g01ftf Example Text Example Data 21 nagf_stat_inv_cdf_landau Landau inverse function $\Psi \left(x\right)$ g01gbf Example Text Example Data 14 nagf_stat_prob_students_t_noncentral Computes probabilities for the non-central Student's $t$-distribution g01gcf Example Text Example Data 14 nagf_stat_prob_chisq_noncentral Computes probabilities for the non-central ${\chi }^{2}$ distribution g01gdf Example Text Example Data 14 nagf_stat_prob_f_noncentral Computes probabilities for the non-central $F$-distribution g01gef Example Text Example Data 14 nagf_stat_prob_beta_noncentral Computes probabilities for the non-central beta distribution g01haf Example Text Example Data 14 nagf_stat_prob_bivariate_normal Computes probability for the bivariate Normal distribution g01hbf Example Text Example Data 15 nagf_stat_prob_multi_normal Computes probabilities for the multivariate Normal distribution g01hcf Example Text Example Data 23 nagf_stat_prob_bivariate_students_t Computes probabilities for the bivariate Student's $t$-distribution g01hdf Example Text Example Data 24 nagf_stat_prob_multi_students_t Computes the probability for the multivariate Student's $t$-distribution g01jcf Example Text Example Data 14 nagf_stat_prob_chisq_noncentral_lincomb Computes probability for a positive linear combination of ${\chi }^{2}$ variables g01jdf Example Text Example Data 15 nagf_stat_prob_chisq_lincomb Computes lower tail probability for a linear combination of (central) ${\chi }^{2}$ variables g01kaf Example Text Example DataExample Plot 23 nagf_stat_pdf_normal Calculates the value for the probability density function of the Normal distribution at a chosen point g01kff Example Text Example DataExample Plot 23 nagf_stat_pdf_gamma Calculates the value for the probability density function of the gamma distribution at a chosen point g01kkf Example Text Example DataExample Plot 24 nagf_stat_pdf_gamma_vector Computes a vector of values for the probability density function of the gamma distribution g01kqf Example Text Example DataExample Plot 24 nagf_stat_pdf_normal_vector Computes a vector of values for the probability density function of the Normal distribution g01lbf Example Text Example Data 24 nagf_stat_pdf_multi_normal_vector Computes a vector of values for the probability density function of the multivariate Normal distribution g01mbf Example Text Example Data 15 nagf_stat_mills_ratio Computes reciprocal of Mills' Ratio g01mtf Example Text Example Data 21 nagf_stat_pdf_landau Landau density function $\varphi \left(\lambda \right)$ g01muf Example Text Example Data 21 nagf_stat_pdf_vavilov Vavilov density function ${\varphi }_{V}\left(\lambda ;\kappa ,{\beta }^{2}\right)$ g01naf Example Text Example Data 16 nagf_stat_moments_quad_form Cumulants and moments of quadratic forms in Normal variables g01nbf Example Text Example Data 16 nagf_stat_moments_ratio_quad_forms Moments of ratios of quadratic forms in Normal variables, and related statistics g01ptf Example Text Example Data 21 nagf_stat_pdf_landau_moment1 Landau first moment function ${\Phi }_{1}\left(x\right)$ g01qtf Example Text Example Data 21 nagf_stat_pdf_landau_moment2 Landau second moment function ${\Phi }_{2}\left(x\right)$ g01rtf Example Text Example Data 21 nagf_stat_pdf_landau_deriv Landau derivative function ${\varphi }^{\prime }\left(\lambda \right)$ g01saf Example Text Example Data 24 nagf_stat_prob_normal_vector Computes a vector of probabilities for the standard Normal distribution g01sbf Example Text Example Data 24 nagf_stat_prob_students_t_vector Computes a vector of probabilities for the Student's $t$-distribution g01scf Example Text Example Data 24 nagf_stat_prob_chisq_vector Computes a vector of probabilities for ${\chi }^{2}$ distribution g01sdf Example Text Example Data 24 nagf_stat_prob_f_vector Computes a vector of probabilities for $F$-distribution g01sef Example Text Example Data 24 nagf_stat_prob_beta_vector Computes a vector of probabilities for the beta distribution g01sff Example Text Example Data 24 nagf_stat_prob_gamma_vector Computes a vector of probabilities for the gamma distribution g01sjf Example Text Example Data 24 nagf_stat_prob_binomial_vector Computes a vector of probabilities for the binomial distribution g01skf Example Text Example Data 24 nagf_stat_prob_poisson_vector Computes a vector of probabilities for the Poisson distribution g01slf Example Text Example Data 24 nagf_stat_prob_hypergeom_vector Computes a vector of probabilities for the hypergeometric distribution g01taf Example Text Example Data 24 nagf_stat_inv_cdf_normal_vector Computes a vector of deviates for the standard Normal distribution g01tbf Example Text Example Data 24 nagf_stat_inv_cdf_students_t_vector Computes a vector of deviates for Student's $t$-distribution g01tcf Example Text Example Data 24 nagf_stat_inv_cdf_chisq_vector Computes a vector of deviates for ${\chi }^{2}$ distribution g01tdf Example Text Example Data 24 nagf_stat_inv_cdf_f_vector Computes a vector of deviates for $F$-distribution g01tef Example Text Example Data 24 nagf_stat_inv_cdf_beta_vector Computes a vector of deviates for the beta distribution g01tff Example Text Example Data 24 nagf_stat_inv_cdf_gamma_vector Computes a vector of deviates for the gamma distribution g01waf Example Text Example DataExample Plot 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
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017