simulated_data {FunctionalCalibration}R Documentation

Simulated Data

Description

This is a simulated dataset designed to illustrate the functionalities of the package. It contains 100 samples of aggregated data generated from two functions, \alpha_1(x) and \alpha_2(x), with added Gaussian noise N(0, 0.1).

The functions used in the simulation are:

\alpha_1(x) = \sin(5x) e^{-x^2} \quad \alpha_2(x) = \begin{cases} -2, & x < 0 \\ 0, & 0 \leq x < 1.5 \\ 3, & x \geq 1.5 \end{cases}

The simulations were performed over an equally spaced grid of 1024 points in the interval [-1, 2]. These functions were linearly combined using random concentrations to generate the samples, with the addition of Gaussian noise.

Usage

simulated_data

Format

An object of class list of length 4.

Value

data

A data frame with 1024 rows and 100 columns.
Each column represents one sample of the aggregated functions with Gaussian noise N(0, 0.1).

weigths

A data frame with 2 rows and 100 columns.
Each column contains the random concentrations used to aggregate the two functions in each sample.

x

A numeric vector of length 1024.
The grid of x-values used in the simulation, equally spaced from -1 to 2.

alphas

A data frame with 1024 rows and 2 columns.
The true values of the functions \alpha_1(x) and \alpha_2(x) evaluated over the x grid.


[Package FunctionalCalibration version 1.0.0 Index]