| hermiter-package {hermiter} | R Documentation |
Efficient Sequential and Batch Estimation of Univariate and Bivariate Probability Density Functions and Cumulative Distribution Functions along with Quantiles (Univariate) and Nonparametric Correlation (Bivariate)
Description
Facilitates estimation of full univariate and bivariate probability density functions and cumulative distribution functions along with full quantile functions (univariate) and nonparametric correlation (bivariate) using Hermite series based estimators. These estimators are particularly useful in the sequential setting (both stationary and non-stationary) and one-pass batch estimation setting for large data sets. Based on: Stephanou, Michael, Varughese, Melvin and Macdonald, Iain. "Sequential quantiles via Hermite series density estimation." Electronic Journal of Statistics 11.1 (2017): 570-607 <doi:10.1214/17-EJS1245>, Stephanou, Michael and Varughese, Melvin. "On the properties of Hermite series based distribution function estimators." Metrika (2020) <doi:10.1007/s00184-020-00785-z> and Stephanou, Michael and Varughese, Melvin. "Sequential estimation of Spearman rank correlation using Hermite series estimators." Journal of Multivariate Analysis (2021) <doi:10.1016/j.jmva.2021.104783>.
Package Content
Index of help topics:
IQR Estimates the Interquartile range (IQR)
IQR.default Estimates the Interquartile range (IQR)
IQR.hermite_estimator_univar
Estimates the Interquartile range (IQR)
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.
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_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_integral_val Outputs lower integral of the orthonormal
Hermite functions
hermite_integral_val_upper
Outputs upper 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.
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)
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
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
Maintainer
Michael Stephanou <michael.stephanou@gmail.com>
Author(s)
Michael Stephanou [aut, cre], Melvin Varughese [ctb]
[Package hermiter version 2.3.1 Index]