# Efficient Sequential and Batch Estimation of Univariate and Bivariate Probability Density Functions and Cumulative Distribution Functions along with Quantiles (Univariate) and Nonparametric Correlation (Bivariate)

## Documentation for package ‘hermiter’ version 2.3.1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

hermiter-package | Efficient Sequential and Batch Estimation of Univariate and Bivariate Probability Density Functions and Cumulative Distribution Functions along with Quantiles (Univariate) and Nonparametric Correlation (Bivariate)

cor

A wrapper around the stats::cor function adding two additional methods, namely method = "hermite.spearman" and method = "hermite.kendall" (can be abbreviated). The input parameters and output value semantics closely match the stats::cor method for easy interchange. If neither the "hermite.spearman" nor the "hermite.kendall" method is selected, then this function will call stats::cor with the arguments provided.

cum_prob | Estimates the cumulative probability at one or more x values
cum_prob.hermite_estimator_bivar | Estimates the cumulative probabilities for a matrix of 2-d x values
cum_prob.hermite_estimator_univar | Estimates the cumulative probability for a vector of x values
dens | Estimates the probability density at one or more x values
dens.hermite_estimator_bivar | Estimates the probability densities for a matrix of 2-d x values
dens.hermite_estimator_univar | Estimates the probability density for a vector of x values
density.hermite_estimator_bivar | Creates an object summarizing the bivariate PDF with associated generic methods print and plot.
density.hermite_estimator_univar | Creates an object summarizing the PDF with associated generic methods print and plot.
gauss_hermite_quad_100 | Calculates \int_{-Inf}^{Inf} f(x) e^{-x^2} dx using Gauss-Hermite quadrature with 100 terms.
hcdf | Creates an object summarizing the CDF with associated generic methods print, plot and summary.
hcdf.hermite_estimator_bivar | Creates an object summarizing the bivariate CDF with associated generic methods print, plot and summary.
hcdf.hermite_estimator_univar | Creates an object summarizing the CDF with associated generic methods print, plot and summary.
hermiter | Efficient Sequential and Batch Estimation of Univariate and Bivariate Probability Density Functions and Cumulative Distribution Functions along with Quantiles (Univariate) and Nonparametric Correlation (Bivariate)
hermite_estimator | A class to sequentially estimate univariate and bivariate pdfs and cdfs along with quantile functions in the univariate setting and nonparametric correlations in the bivariate setting.
hermite_estimator_bivar | A class to sequentially estimate bivariate pdfs, cdfs and nonparametric correlations
hermite_estimator_univar | A class to sequentially estimate univariate pdfs, cdfs and quantile functions
hermite_function | Outputs orthonormal Hermite functions
hermite_function_N | Convenience function to output orthonormal Hermite functions The method calculates the orthonormal Hermite functions, h_k(x) from k=0,...,N for the vector of values, x.
hermite_function_sum_N | Convenience function to output the sum of orthonormal Hermite functions The method calculates the sum of orthonormal Hermite functions, sum_{i} h_k(x_{i}) from k=0,...,N for the vector of values, x.
hermite_function_sum_serial | Outputs the sum of orthonormal Hermite functions
hermite_integral_val | Outputs lower integral of the orthonormal Hermite functions
hermite_integral_val_upper | Outputs upper integral of the orthonormal Hermite functions
hermite_int_full | Convenience function to output the integral of the orthonormal Hermite functions on the full domain
hermite_int_full_domain | Outputs integral of the orthonormal Hermite functions on the full domain
hermite_int_lower | Convenience function to output a definite integral of the orthonormal Hermite functions
hermite_int_upper | Convenience function to output a definite integral of the orthonormal Hermite functions
hermite_normalization | Outputs Hermite normalization factors
hermite_normalization_N | Convenience function to output Hermite normalization factors
hermite_polynomial | Outputs physicist version of Hermite Polynomials
hermite_polynomial_N | Convenience function to output physicist Hermite polynomials The method calculates the physicist version of Hermite polynomials, H_k(x) from k=0,...,N for the vector of values, x.
initialize_batch_bivar | Initializes the Hermite series based estimator with a batch of data
initialize_batch_univar | Initializes the Hermite series based estimator with a batch of data
IQR | Estimates the Interquartile range (IQR)
IQR.default | Estimates the Interquartile range (IQR)
IQR.hermite_estimator_univar | Estimates the Interquartile range (IQR)
kendall | Estimates the Kendall rank correlation coefficient
kendall.hermite_estimator_bivar | Estimates the Kendall rank correlation coefficient
median.hermite_estimator_univar | Estimates the median
merge_hermite | Merges a list of Hermite estimators
merge_hermite_bivar | Merges a list of bivariate Hermite estimators
merge_hermite_univar | Merges a list of Hermite estimators
merge_moments_and_count_bivar | Internal method to consistently merge the number of observations, means and variances of two bivariate Hermite estimators
merge_moments_and_count_univar | Internal method to consistently merge the number of observations, means and variances of two Hermite estimators
merge_pair | Merges two Hermite estimators
merge_pair.hermite_estimator_bivar | Merges two bivariate Hermite estimators
merge_pair.hermite_estimator_univar | Merges two Hermite estimators
merge_standardized_helper_bivar | Internal method to merge a list of standardized bivariate Hermite estimators
merge_standardized_helper_univar | Internal method to merge a list of standardized Hermite estimators
plot.hcdf_bivar | Plots the hcdf_bivar object as output by the hcdf function when evaluated on a hermite_estimator_bivar object.
plot.hcdf_univar | Plots the hcdf_univar object as output by the hcdf function when evaluated on a hermite_estimator_univar object.
plot.hdensity_bivar | Plots the hdensity_bivar object as output by the density function when evaluated on a hermite_estimator_bivar object.
plot.hdensity_univar | Plots the hdensity_univar object as output by the density function when evaluated on a hermite_estimator_univar object.
print.hcdf_bivar | Prints the hcdf_bivar object as output by the hcdf function when evaluated on a hermite_estimator_bivar object.
print.hcdf_univar | Prints the hcdf_univar object as output by the hcdf function when evaluated on a hermite_estimator_univar object.
print.hdensity_bivar | Prints the hdensity_bivar object as output by the density function when evaluated on a hermite_estimator_bivar object.
print.hdensity_univar | Prints the hdensity_univar object as output by the density function when evaluated on a hermite_estimator_univar object.
print.hermite_estimator_bivar | Prints bivariate hermite_estimator object.
print.hermite_estimator_univar | Prints univariate hermite_estimator object.
quant | Estimates the quantiles at a vector of probability values
quant.hermite_estimator_univar | Estimates the quantiles at a vector of probability values
quantile.hermite_estimator_univar | Estimates the quantiles at a vector of probability values
spearmans | Estimates the Spearman's rank correlation coefficient
spearmans.hermite_estimator_bivar | Estimates the Spearman's rank correlation coefficient
standardizeInputs | Standardizes the observation x and updates the online moment inputs
standardizeInputsEW | Standardizes the observation x and updates the online moment inputs
summary.hcdf_bivar | Summarizes the hcdf_bivar object as output by the hcdf function when evaluated on a hermite_estimator_bivar object.
summary.hcdf_univar | Summarizes the hcdf_univar object as output by the hcdf function when evaluated on a hermite_estimator_univar object.
summary.hermite_estimator_bivar | Summarizes bivariate hermite_estimator object.
summary.hermite_estimator_univar | Summarizes univariate hermite_estimator object.
update_sequential | Updates the Hermite series based estimator sequentially
update_sequential.hermite_estimator_bivar | Updates the Hermite series based estimator sequentially
update_sequential.hermite_estimator_univar | Updates the Hermite series based estimator sequentially