simu_data {fdasrvf}

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({e^{a_i(t+3)/6} -1 \over e^{a_i} - 1}) - 3 if a_i \neq 0, otherwise \gamma_i = \gamma_{id} (gamma_{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.