hermite_integral_val_upper

The method calculates \(\int_{x}^{\infty} h_k(t) dt\) 
for \(k=0,\dots,N\) and the vector of values x.

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>.

Michael Stephanou

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)

Melvin Varughese

hermite_integral_val_upper function

<dl><dt>N</dt>
<dd>An integer number.</dd>
<dt>x</dt>
<dd>A numeric vector.</dd>
<dt>hermite_function_mat</dt>
<dd>A numeric matrix of Hermite function values 
generated by the function hermite_function.</dd></dl>

Arguments

Michael Stephanou &lt;michael.stephanou@gmail.com&gt;

Author

Outputs upper integral of the orthonormal Hermite functions — hermite_integral_val_upper

<dl>

<dt>N</dt>
<dd>An integer number.</dd>


<dt>x</dt>
<dd>A numeric vector.</dd>


<dt>hermite_function_mat</dt>
<dd>A numeric matrix of Hermite function values 
generated by the function hermite_function.</dd>

</dl>

hermite_integral_val_upper: Outputs upper integral of the orthonormal Hermite functions

Description

Usage

Value

Arguments

Author