FMM (version 0.4.1)

generateFMM: Simulating data from FMM models

Description

generateFMM() simulates data from a FMM model defined by parameters M, A, \(\alpha\), \(\beta\) and \(\omega\).

Usage

generateFMM(
  M,
  A,
  alpha,
  beta,
  omega,
  from = 0,
  to = 2 * pi,
  length.out = 200,
  plot = TRUE,
  outvalues = TRUE,
  sigmaNoise = 0
)

Value

When outvalues = TRUE a list of with the following components is returned:

input

a list with the input parameters M, A, alpha, beta and omega.

t

a numeric vector with the time points at each data is simulated.

y

a numeric vector with the data simulated.

When plot = TRUE a scatter plot of y vs t is drawn.

Arguments

M

A numeric vector which contains the value of the intercept parameter M.

A

A positive numeric vector which contains the value of the FMM wave amplitude parameter A.

alpha

A numeric vector which contains the value of the FMM wave phase translation parameter \(\alpha\).

beta

A numeric vector which contains the value of the FMM wave skewness parameter \(\beta\).

omega

A numeric vector which contains the value of the FMM wave kurtosis parameter \(\omega\). omega parameter must be between 0 and 1.

from

A numeric value which contains the initial time point of the simulated data. By default, it is 0.

to

A numeric value which contains the final time point of the simulated data. By default, it is \(2\pi\).

length.out

A non-negative number wich contains the desired length of the simulation. By default, it is 100.

plot

A logical value indicating whether the simulated data should be drawn on a plot. By default, it is TRUE.

outvalues

A logical value indicating whether the numerical simulation should be return. By default, it is TRUE.

sigmaNoise

A non-negative number which contains the standard deviation of the gaussian noise to be added. Its default value is zero equivalent to a simulation set-up without noise.

Details

To simulate a multicomponent FMM model, arguments A, alpha, beta and omega are vectors of length \(m\), where \(m\) represents the number of FMM waves. With different lengths, the smaller vectors will be replicate until thay are the same length as the longest vector.

With sigmaNoise = s, s>0, the generateFMM function uses rnorm(length.out, 0, sigmaNoise) to create the normally distributed noise and adds it to the simulated values.

References

Rueda C, Larriba Y, Peddada SD (2019). Frequency Modulated Moebius Model Accurately Predicts Rhythmic Signals in Biological and Physical Sciences. Scientific reports, 9 (1), 18701. https://www.nature.com/articles/s41598-019-54569-1

Examples

# Simulate data from a monocomponent FMM model. A plot with the simulated model is shown
generateFMM(M = 2,A = 3,alpha = 1.5,beta = 2.3, omega = 0.1, outvalues = FALSE)

# Add a gaussian noise with standard deviation 0.3. The numeric results are returned
generateFMM(M = 2, A = 3, alpha = 1.5, beta = 2.3, omega = 0.1,
            sigmaNoise = 0.3, plot = FALSE, outvalues = TRUE)

# Simulate data from a multicomponent FMM model with two FMM waves
# both with amplitude parameter = 2
generateFMM(M = 0, A = rep(2, 2), alpha = c(1.5, 3.4), beta = c(0.2, 2.3), omega = c(0.1, 0.2))