Appendix A, Alphabetical Summary of Routines

Analyzes a balanced complete experimental design for a fixed, random, or mixed model.

Analyzes a balanced incomplete block design or a balanced lattice design.

Computes the sample autocorrelation function of a stationary time series.

Returns a character given its ASCII value

Produces population and cohort life tables.

Performs an Anderson‑Darling test for normality.

Evaluates the cumulative distribution function of the one‑sided Kolmogorov‑Smirnov goodness‑of‑fit D+ or D− test statistic based on continuous data for one sample.

Evaluates the cumulative distribution function of the Kolmogorov‑Smirnov goodness‑of‑fit D test statistic based on continuous data for two samples

Analyzes a Latin square design.

Evaluates the lognormal cumulative probability distribution function.

This function evaluates the inverse of the lognormal cumulative probability distribution function.

Evaluates the lognormal probability density function.

Retrieves machine constants.

Evaluates Mill's ratio (the ratio of the ordinate to the upper tail area of the standardized normal distribution).

Analyzes a completely nested random model with possibly unequal numbers in the subgroups.

Evaluates the normal probability density function.

Evaluates the standard normal (Gaussian) cumulative distribution function.

Evaluates the inverse of the standard normal (Gaussian) cumulative distribution function.

Analyzes a balanced n‑way classification model with fixed effects.

Analyzes a one‑way classification model with covariates.

Analyzes a one‑way classification model.

Calculates the rational power spectrum for an ARMA model.

Computes method of moments estimates of the autoregressive parameters of an ARMA model.

Analyzes a randomized block design or a two‑way balanced design.

Automatically identifies time series outliers, determines parameters of a multiplicative seasonal ARIMA (p,0,q) × (0,d,0)s model, and produces forecasts that incorporate the effects of outliers whose effects persist beyond the end of the series.

Automatic selection and fitting of a multivariate autoregressive time series model using Akaike’s Multivariate Final Prediction Error (MFPE) criteria.

Automatic selection and fitting of a univariate autoregressive time series model using Akaike’s Final Prediction Error (FPE) criteria.

Automatic selection and fitting of a multivariate autoregressive time series model.

Estimates structural breaks in non‑stationary univariate time series.

Allows for a decomposition of a time series into trend, seasonal, and an error component.

Performs a forward or an inverse Box‑Cox (power) transformation.

Evaluates the beta cumulative distribution function.

Evaluates the inverse of the beta cumulative distribution function.

This function evaluates the noncentral beta cumulative distribution function (CDF) .

This function evaluates the inverse of the noncentral beta cumulative distribution function (CDF).

This function evaluates the noncentral beta probability density function.

Evaluates the beta probability density function.

Performs a Bhapkar V test.

Evaluates the binomial cumulative distribution function.

Estimates the parameter p of the binomial distribution.

Evaluates the binomial probability density function.

Evaluates the bivariate normal cumulative distribution function.

Prints boxplots for one or more samples.

Computes the biserial correlation coefficient for a dichotomous variable and a classification variable.

Given an input array of deviate values, generates a canonical correlation array.

Performs canonical correlation analysis from a data matrix.

Performs canonical correlation analysis from a variance‑covariance matrix or a correlation matrix.

Computes the sample cross‑correlation function of two stationary time series.

Prints a plot of two sample cumulative distribution functions.

Prints a sample cumulative distribution function (CDF), a theoretical CDF, and confidence band information.

Computes a matrix of dissimilarities (or similarities) between the columns (or rows) of a matrix.

Constructs an equivalent completely testable multivariate general linear hypothesis HBU = G from a partially testable hypothesis HpBU = Gp.

Computes an upper triangular factorization of a real symmetric nonnegative definite matrix.

Evaluates the chi‑squared cumulative distribution function.

Performs a chi‑squared goodness‑of‑fit test.

Evaluates the inverse of the chi‑squared cumulative distribution function.

Evaluates the chi‑squared probability density function.

Computes a confidence interval on a variance component estimated as proportional to the difference in two mean squares in a balanced complete experimental design.

Performs a hierarchical cluster analysis given a distance matrix.

Calculates and tests the significance of the Kendall coefficient of concordance.

Computes cluster membership for a hierarchical cluster tree.

Computes the variance‑covariance or correlation matrix.

Computes a pooled variance‑covariance matrix from the observations.

Computes the cross periodogram of two stationary time series using a fast Fourier transform.

Returns CPU time used in seconds.

Evaluates the noncentral chi‑squared cumulative distribution function.

Evaluates the inverse of the noncentral chi‑squared cumulative function.

This function evaluates the noncentral chi‑squared probability density function.

Estimates the nonnormalized cross‑spectral density of two stationary time series using a spectral window given the time series data.

Estimates the nonnormalized cross‑spectral density of two stationary time series using a spectral window given the spectral densities and cross periodogram.

Computes cell frequencies, cell means, and cell sums of squares for multivariate data.

Estimates the nonnormalized cross‑spectral density of two stationary time series using a weighted cross periodogram given the time series data.

Estimates the nonnormalized cross‑spectral density of two stationary time series using a weighted cross periodogram given the spectral densities and cross periodogram.

Computes partial association statistics for log‑linear models in a multidimensional contingency table.

Performs a chi‑squared analysis of a two‑way contingency table.

Computes Fisher’s exact test probability and a hybrid approximation to the Fisher exact test probability for a contingency table using the network algorithm.

Analyzes categorical data using logistic, Probit, Poisson, and other generalized linear models.

Computes model estimates and associated statistics for a hierarchical log‑linear model.

Computes model estimates and covariances in a fitted log‑linear model.

Computes exact probabilities in a two‑way contingency table.

Performs generalized Mantel‑Haenszel tests in a stratified contingency table.

Estimates the bivariate normal correlation coefficient using a contingency table.

Computes contrast estimates and sums of squares.

Builds hierarchical log‑linear models using forward selection, backward selection, or stepwise selection.

Performs a chi‑squared analysis of a 2 by 2 contingency table.

Performs a generalized linear least squares analysis of transformed probabilities in a two‑dimensional contingency table.

Performs a Cramer‑von Mises test for normality.

Performs a triplets test.

Performs nonparametric probability density function estimation by the kernel method.

Performs nonparametric probability density function estimation by the penalized likelihood method.

Estimates a probability density function at specified points using linear or cubic interpolation.

Difference a time series.

Computes the Dirichlet kernel.

See AMACH.

Uses Fisher’s linear discriminant analysis method to reduce the number of variables.

Computes Gaussian kernel estimates of a univariate density via the fast Fourier transform over a fixed interval.

Performs a linear or a quadratic discriminant function analysis among several known groups.

Evaluates the expected value of a normal order statistic.

Computes empirical quantiles.

Sets error handler default print and stop actions.

Estimates missing values in a time series.

Evaluates the exponential cumulative distribution function.

Evaluates the inverse of the exponential cumulative distribution function.

This function evaluates the exponential probability density function.

Evaluates the extreme value cumulative distribution function.

Evaluates the inverse of the extreme value cumulative distribution function.

Extracts initial factor‑loading estimates in factor analysis.

Frees the structure containing information about the Faure sequence.

Computes a shuffled Faure sequence.

Shuffled Faure sequence initialization.

Computes a matrix of factor score coefficients for input to the following IMSL function (FSCOR).

Evaluates the F cumulative distribution function.

Computes a direct oblimin rotation of a factor‑loading matrix.

Computes the Fejér kernel.

Computes direct oblique rotation according to a generalized fourth‑degree polynomial criterion.

Computes an oblique rotation of an unrotated factor‑loading matrix using the Harris‑Kaiser method.

Computes the image transformation matrix.

Evaluates the inverse of the F cumulative distribution function.

Noncentral F cumulative distribution function.

This function evaluates the inverse of the noncentral F cumulative distribution function (CDF).

This function evaluates the noncentral F cumulative distribution function (CDF).

Computes an orthogonal Procrustes rotation of a factor‑loading matrix using a target matrix.

Evaluates the F probability density function.

Computes an oblique Promax or Procrustes rotation of a factor‑loading matrix using a target matrix, including pivot and power vector options.

Performs Friedman’s test for a randomized complete block design.

Tallies multivariate observations into a multi‑way frequency table.

Computes commonalities and the standardized factor residual correlation matrix

Computes an orthogonal rotation of a factor‑loading matrix using a generalized orthomax criterion, including quartimax, varimax, and equamax rotations.

Computes the factor structures and the variance explained by each factor.

Evaluates the gamma cumulative distribution function.

Evaluates the inverse of the gamma cumulative distribution function.

Evaluates the gamma probability density function.

Computes estimates of the parameters of a GARCH (p,q) model.

Evaluates a general continuous cumulative distribution function given ordinates of the density.

Evaluates the inverse of a general continuous cumulative distribution function given ordinates of the density.

Gets the unique values of each classification variable.

Generates centered variables, squares, and crossproducts.

Retrieves a commonly analyzed data set.

Evaluates the geometric cumulative probability distribution function.

Evaluates the inverse of the geometric cumulative probability distribution function.

Evaluates the geometric probability density function.

Evaluates the inverse of a general continuous cumulative distribution function given in a subprogram.

Solves a triangular (possibly singular) set of linear systems and/or compute a generalized inverse of an upper triangular matrix.

Generates regressors for a general linear model.

Computes basic statistics from grouped data.

Performs nonparametric hazard rate estimation using kernel functions. Easy‑to‑use version of the previous IMSL subfunction (HAZRD).

Performs nonparametric hazard rate estimation using kernel functions and quasi‑likelihoods.

Performs hazard rate estimation over a grid of points using a kernel function.

Prints a horizontal histogram

Evaluates the hypergeometric cumulative distribution function.

Returns the integer ASCII value of a character argument.

Returns the ASCII value of a character converted to uppercase.

Computes the day of the week for a given date.

Retrieves the code for an informational error.

Checks if a floating‑point number is NaN (not a number).

Compares two character strings using the ASCII collating sequence without regard to case.

Determines the position in a string at which a given character sequence begins without regard to case.

Retrieves integer machine constants.

Performs an includance test.

Computes estimates of the impulse response weights and noise series of a univariate transfer function model.

Performs Kalman filtering and evaluate the likelihood function for the state‑space model.

Computes Kaplan‑Meier estimates of survival probabilities in stratified samples.

Computes and tests Kendall’s rank correlation coefficient.

Computes the frequency distribution of the total score in Kendall’s rank correlation coefficient.

Performs a K‑means (centroid) cluster analysis.

Maximum likelihood or least‑squares estimates for principle components from one or more matrices.

Performs a Kruskal‑Wallis test for identical population medians.

Performs a Kolmogorov‑Smirnov one‑sample test for continuous distributions.

Performs a Kolmogorov‑Smirnov two‑sample test.

Prints Kaplan‑Meier estimates of survival probabilities in stratified samples.

Produces a letter value summary.

Performs Lilliefors test for an exponential or normal distribution.

Computes method of moments estimates of the moving average parameters of an ARMA model.

Exacts maximum likelihood estimation of the parameters in a univariate ARMA (auto‑regressive, moving average) time series model.

Computes the multichannel cross‑correlation function of two mutually stationary multichannel time series.

Computes an upper triangular factorization of a real symmetric matrix A plus a diagonal matrix D, where D is determined sequentially during the Cholesky factorization in order to make A + D nonnegative definite.

Computes a median polish of a two‑way table.

Computes least squares estimates of a linear regression model for a multichannel time series with a specified base channel.

Calculates maximum likelihood estimates for the parameters of one of several univariate probability distributions.

Obtains normalized product‑moment (double centered) matrices from dissimilarity matrices.

Computes distances in a multidimensional scaling model.

Performs individual‑differences multidimensional scaling for metric data using alternating least squares.

Computes initial estimates in multidimensional scaling models.

Transforms dissimilarity/similarity matrices and replace missing values by estimates to obtain standardized dissimilarity matrices.

Computes various stress criteria in multidimensional scaling.

Computes a test for the independence of k sets of multivariate normal variables.

Computes Mardia’s multivariate measures of skewness and kurtosis and tests for multivariate normality.

Moves any rows of a matrix with the IMSL missing value code NaN (not a number) in the specified columns to the last rows of the matrix.

Retrieves an error type for the most recently called IMSL function.

Performs the Noether test for cyclical trend.

Computes the number of days from January 1, 1900, to the given date.

Gives the date corresponding to the number of days since January 1, 1900.

Searches a k-d tree for the k nearest neighbors of a key.

Performs a k nearest neighbor discrimination.

Computes maximum likelihood estimates of the mean and variance from grouped and/or censored normal data.

Computes Box‑Jenkins forecasts and their associated probability limits for a nonseasonal ARMA model.

Computes least squares estimates of parameters for a nonseasonal ARMA model.

Computes preliminary estimates of the autoregressive and moving average parameters of an ARMA model.

Generates orthogonal polynomials with respect to x values and specified weights.

Allows for multiple channels for both the controlled and manipulated variables.

Determines order statistics.

Computes the sample partial autocorrelation function of a stationary time series.

Performs a pairs test.

Computes partial correlations or covariances from the covariance or correlation matrix.

Permutes the rows or columns of a matrix.

Rearranges the elements of an array as specified by a permutation.

Computes the periodogram of a stationary time series using a fast Fourier transform.

Sets or retrieves page width and length for printing.

Analyzes time event data via the proportional hazards model.

Prints a plot of up to ten sets of points.

Performs partial least squares regression for one or more response variables and a set of one or more predictor variables.

Evaluates the Poisson cumulative distribution function.

Estimates the parameter of the Poisson distribution.

Evaluates the Poisson probability density function.

Computes principal components from a variance‑covariance matrix or a correlation matrix.

Prints a probability plot.

Performs a Cochran Q test for related observations.

Evaluates the Rayleigh cumulative distribution function.

Evaluates the inverse of the Rayleigh cumulative distribution function.

Evaluates the Rayleigh probability density function.

Computes the ranks, normal scores, or exponential scores for a vector of observations.

Computes a robust estimate of a covariance matrix and mean vector.

Selects the best multiple linear regression models.

Computes case statistics and diagnostics given data points, coefficient estimates , and the R matrix for a fitted general linear model.

Computes case statistics for a polynomial regression model given the fit based on orthogonal polynomials.

Generates an orthogonal central composite design.

Fits a multiple linear regression model given the variance‑covariance matrix.

Computes the estimated variance‑covariance matrix of the estimated regression coefficients given the R matrix.

Fits a polynomial curve using least squares.

Fits a univariate, non seasonal ARIMA time series model with the inclusion of one or more regression variables.

Fits an orthogonal polynomial regression model.

Fits a multivariate linear regression model via fast Givens transformations.

Fits a multivariate general linear model.

Computes the matrix of sums of squares and crossproducts for the multivariate general linear hypothesis HBU = G given the coefficient estimates and the R matrix.

Performs tests for a multivariate general linear hypothesis HBU = G given the hypothesis sums of squares and crossproducts matrix SH and the error sums of squares and crossproducts matrix SE.

Performs response control given a fitted simple linear regression model.

Performs inverse prediction given a fitted simple linear regression model.

Fits a multiple linear regression model using the least absolute values criterion.

Fits a multivariate linear regression model with linear equality restrictions HΒ = G imposed on the regression parameters given results from IMSL function RGIVN after IDO = 1 and IDO = 2 and prior to IDO = 3.

Fits a line to a set of data points using least squares.

Fits a multiple linear regression model using the Lp norm criterion.

Fits a multiple linear regression model using the minimax criterion.

Computes a lack‑of‑fit test based on exact replicates for a fitted regression model.

Computes a lack‑of‑fit test based on near replicates for a fitted regression model.

Fits a multiple linear regression model using least squares.

Generates a time series from a specified ARMA model.

Generates pseudorandom numbers from a beta distribution.

Generates pseudorandom numbers from a binomial distribution.

Generates pseudorandom numbers from a chi‑squared distribution.

Generates pseudorandom numbers from a Cauchy distribution.

Generates a pseudorandom orthogonal matrix or a correlation matrix.

Generates pseudorandom numbers from a multivariate distribution determined from a given sample.

Generates pseudorandom numbers from a standard exponential distribution.

Generates pseudorandom numbers from a mixture of two exponential distributions.

Generates pseudorandom numbers from an extreme value distribution.

Generates pseudorandom numbers from the F distribution.

Generates pseudorandom numbers from a standard gamma distribution.

Sets up table to generate pseudorandom numbers from a general continuous distribution.

Generates pseudorandom numbers from a general continuous distribution.

Generates pseudorandom numbers from a general discrete distribution using an alias method.

Sets up table to generate pseudorandom numbers from a general discrete distribution.

Generates pseudorandom numbers from a general discrete distribution using a table lookup method.

Retrieves the current value of the array used in the IMSL GFSR random number generator.

Generates pseudorandom numbers from a geometric distribution.

Retrieves the current value of the table in the IMSL random number generators that use shuffling.

Retrieves the current value of the seed used in the IMSL random number generators.

Generates pseudorandom numbers from a hypergeometric distribution.

Initializes the 32‑bit Mersenne Twister generator using an array.

Retrieves the current table used in the 32‑bit Mersenne Twister generator.

Sets the current table used in the 32‑bit Mersenne Twister generator.

Initializes the 32‑bit Mersenne Twister generator using an array.

Retrieves the current table used in the 64‑bit Mersenne Twister generator

Sets the current table used in the 64‑bit Mersenne Twister generator.

Determines a seed that yields a stream beginning 100,000 numbers beyond the beginning of the stream yielded by a given seed used in IMSL multiplicative congruential generators (with no shufflings).

Performs the Wilcoxon rank sum test.

Generates pseudorandom numbers from a logarithmic distribution.

Fits a nonlinear regression model.

Generates pseudorandom numbers from a lognormal distribution.

Generates pseudorandom numbers from a multinomial distribution.

Generates pseudorandom numbers from a multivariate Gaussian Copula distribution.

Generates a length N output vector R of pseudorandom numbers from a Student’s t Copula distribution.

Generates pseudorandom numbers from a multivariate normal distribution.

Generates pseudorandom numbers from a negative binomial distribution.

Generates pseudorandom numbers from a standard normal distribution using an acceptance/rejection method.

Generates a pseudorandom number from a standard normal distribution.

Generates pseudorandom numbers from a standard normal distribution using an inverse CDF method.

Generates pseudorandom order statistics from a standard normal distribution.

Generates pseudorandom numbers from a nonhomogeneous Poisson process.

Retrieves the indicator of the type of uniform random number generator.

Selects the uniform (0, 1) multiplicative congruential pseudorandom number generator.

Generates a pseudorandom permutation.

Generates pseudorandom numbers from a Poisson distribution.

Generates pseudorandom numbers from a Rayleigh distribution.

Initializes the array used in the IMSL GFSR random number generator.

Initializes the table in the IMSL random number generators that use shuffling.

Initializes a random seed for use in the IMSL random number generators.

Generates pseudorandom points on a unit circle or K‑dimensional sphere.

Generates a simple pseudorandom sample of indices.

Generates a simple pseudorandom sample from a finite population.

Generates pseudorandom numbers from a stable distribution.

Generates pseudorandom numbers from a Student’s t distribution.

Generates a pseudorandom two‑way table.

Generates pseudorandom numbers from a triangular distribution on the interval (0,1).

Generates pseudorandom numbers from a uniform (0,1) distribution.

Generates pseudorandom numbers from a discrete uniform distribution.

Generates a pseudorandom number from a uniform (0, 1) distribution.

Generates pseudorandom order statistics from a uniform (0, 1) distribution.

Generates pseudorandom numbers from a von Mises distribution.

Generates pseudorandom numbers from a Weibull distribution.

Analyzes a simple linear regression model.

Reorders rows and columns of a symmetric matrix.

Reorders the responses from a balanced complete experimental design.

Computes diagnostics for detection of outliers and influential data points given residuals and the R matrix for a fitted general linear model.

Analyzes a polynomial regression model.

Computes summary statistics for a polynomial regression model given the fit based on orthogonal polynomials.

Computes statistics related to a regression fit given the coefficient estimates and the R matrix.

Builds multiple linear regression models using forward selection, backward selection, or stepwise selection.

Retrieves a symmetric submatrix from a symmetric matrix.

Computes simultaneous confidence intervals on all pairwise differences of means.

Sorts columns of a real rectangular matrix using keys in rows.

Prints a scatterplot of several groups of data.

Performs the Cox and Stuart sign test for trends in dispersion and location.

Determines an optimal differencing for seasonal adjustments of a time series.

Performs a sign test of the hypothesis that a given value is a specified quantile of a distribution.

Computes statistics for inferences regarding the population proportion and total, given proportion data from a simple random sample.

Computes statistics for inferences regarding the population proportion and total, given proportion data from a stratified random sample.

Computes statistics for inferences regarding the population mean and total using ratio or regression estimation, or inferences regarding the population ratio, given a simple random sample.

Computes statistics for inferences regarding the population mean and total using ratio or regression estimation, given continuous data from a stratified random sample.

Computes statistics for inferences regarding the population mean and total using single‑stage cluster sampling with continuous data.

Computes statistics for inferences regarding the population mean and total, given data from a simple random sample.

Computes statistics for inferences regarding the population mean and total, given data from a stratified random sample.

Computes statistics for inferences regarding the population mean and total, given continuous data from a two‑stage sample with equisized primary units.

Performs Student‑Newman‑Keuls multiple comparison test.

Performs a Wilcoxon signed rank test.

Computes the Wiener forecast operator for a stationary stochastic process.

Performs a Shapiro‑Wilk W‑test for normality.

Searches a sorted vector for a given scalar and return its index.

Sorts rows of a real rectangular matrix using keys in columns.

Searches a character vector, sorted in ascending ASCII order, for a given string and return its index.

Estimates the nonnormalized spectral density of a stationary time series using a spectral window given the time series data.

Estimates the nonnormalized spectral density of a stationary time series using a spectral window given the periodogram.

Estimates survival probabilities and hazard rates for various parametric models.

Prints a stem‑and‑leaf plot.

Analyzes censored survival data using a generalized linear model.

Sorts an integer array by algebraic value.

Sorts an integer array by algebraic value and returns the permutations.

Sorts a real array by algebraic value.

Sorts a real array by algebraic value and returns the permutations.

Estimation of the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the time series data.

Transforms coefficients from a quadratic regression model generated from squares and crossproducts of centered variables to a model using uncentered variables.

Gets today’s date.

Evaluates the Student’s t cumulative distribution function.

Categorizes bivariate data and compute the tetrachoric correlation coefficient.

Computes preliminary estimates of parameters for a univariate transfer function model.

Gets time of day.

Evaluates the inverse of the Student’s t distribution function.

Evaluates the noncentral Student’s t cumulative distribution function.

Evaluates the inverse of the noncentral Student’s t cumulative distribution function.

This function evaluates the noncentral Student's t probability density function.

This function evaluates the Student’s t probability density function.

Prints a binary tree.

Computes Turnbull’s generalized Kaplan‑Meier estimates of survival probabilities in samples with interval censoring.

Detects and determines outliers and simultaneously estimates the model parameters in a time series.

Computes forecasts for an outlier contaminated time series.

Tallies observations into a two‑way frequency table.

Sets or retrieves input or output device unit numbers.

Evaluates the discrete uniform cumulative distribution function.

Evaluates the uniform cumulative distribution function.

Evaluates the inverse of the discrete uniform cumulative distribution function.

Evaluates the discrete uniform probability density function.

Evaluates the inverse of the uniform cumulative distribution function.

Evaluates the uniform probability density function.

Obtains STAT/LIBRARY‑related version and system information.

Prints a vertical histogram with every bar subdivided into two parts.

Evaluates the Weibull cumulative distribution function.

Evaluates the inverse of the Weibull cumulative distribution function.

Evaluates the Weibull probability density function.

Prints an integer rectangular matrix with a given format and labels.

Prints an integer rectangular matrix with integer row and column labels.

Sets or retrieves an option for printing a matrix.

Prints a real rectangular matrix with a given format and labels.