fdasrvf (version 2.3.6)

simu_data: Simulated two Gaussian Dataset

Description

A functional dataset where the individual functions are given by: $y_i(t)=z_{i,1}{e}^{-(t-1.5{)}^2/2}+z_{i,2}{e}^{-(t+1.5{)}^2/2}$, $t\in [-3,3],i=1,2,\dots ,21$, where $z_{i,1}$ and $z_{i,2}$ are i.i.d. normal with mean one and standard deviation 0.25. Each of these functions is then warped according to: ${\gamma }_i(t)=6(\frac{e^{a_i(t+3)/6}-1}{e^{a_i}-1})-3$ if $a_i\ne 0$, otherwise ${\gamma }_i={\gamma }_{id}$ ($gamm{a}_{id}(t)=t$) is the identity warping). The variables are as follows: f containing the 21 functions of 101 samples and time which describes the sampling.

Usage

simu_data

Format

simu_data

A list with 2 components:

• f: A numeric matrix of shape $101\times 21$ storing a sample of size $N=21$ of curves evaluated on a grid of size $M=101$.

• time: A numeric vector of size $M=101$ storing the grid on which the curves f have been evaluated.