generateFMM function

Simulating data from FMM models

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

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

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.

Returns

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.

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.

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))

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