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.
simulated_datadataA data frame with 1024 rows and 100 columns.
Each column represents one sample of the aggregated functions with Gaussian noise \(N(0, 0.1)\).
weigthsA data frame with 2 rows and 100 columns.
Each column contains the random concentrations used to aggregate the two functions in each sample.
xA numeric vector of length 1024.
The grid of x-values used in the simulation, equally spaced from -1 to 2.
alphasA 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.
An object of class list of length 4.