Simulation of trajectories from two samples diverging by a delta function

Simulate n_obs1 trajectories of length n_point in the first sample and n_obs2 trajectories of length n_point in the second sample.

Usage

simul_data(
  n_point,
  n_obs1,
  n_obs2,
  c_val = 0,
  delta_shape = "constant",
  distrib = "normal",
  max_iter = 10000
)

Arguments

n_point: integer value, number of points in the trajectory.
n_obs1: integer value, number of trajectories in the first sample.
n_obs2: integer value, number of trajectories in the second sample.
c_val: numeric value, level of divergence between the two samples.
delta_shape: character string, shape of the divergence between the two samples, among "constant", "linear", "quadratic".
distrib: character string, type of probability distribution used to simulate the data among "normal", "cauchy", "dexp", "student".
max_iter: integer, maximum number of iteration for the iterative simulation process.

Value

A list with the following elements

mat_sample1: numeric matrix of dimension n_point x n_obs1 containing n_obs1 trajectories (in columns) of size n_point (in rows) corresponding to sample 1.
mat_sample2: numeric matrix of dimension n_point x n_obs2 containing n_obs2 trajectories (in columns) of size n_point (in rows) corresponding to sample 2.

References

Zaineb Smida, Lionel Cucala, Ali Gannoun & Ghislain Durif (2022) A median test for functional data, Journal of Nonparametric Statistics, 34:2, 520-553, doi:10.1080/10485252.2022.2064997 , hal-03658578

Author

Zaineb Smida, Ghislain DURIF, Lionel Cucala

Examples

simu_data <- simul_data(
    n_point = 100, n_obs1 = 50, n_obs2 = 75, c_val = 10, 
    delta_shape = "constant", distrib = "normal"
)
str(simu_data)
#> List of 5
#>  $ mat_sample1: num [1:100, 1:50] 10 10 10 10.1 10.1 ...
#>  $ mat_sample2: num [1:100, 1:75] 0 0.036 0.0721 0.108 0.1438 ...
#>  $ c_val      : num 10
#>  $ distrib    : chr "normal"
#>  $ delta_shape: chr "constant"