# irreg.fd: Sample Irregular Functional Data In synfd: Synthesize Dense or Sparse Functional Data/Snippets

## Description

Sample Irregular Functional Data

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```irreg.fd( mu = 0, X = wiener.process(), n = 100, m = 5, sig = NULL, snr = 5, domain = c(0, 1), delta = 1 ) ```

## Arguments

 `mu` function, scalar or a vector defining the mean function; default value: `0`. `X` centered stochastic process defined by a function of the form `X(tObs,n)` and returning `n*length(tObs)` matrix, where each row represents observations from a trajectory. Default value: `wiener.process()`. `n` sample size; default value: `100`. `m` a vector of sampling rate or scalar of average sampling rate or a function of the form `f(n)` generating `n` positive integers; default value: `5`. `sig` standard deviation of measurement errors; if `NULL` then determined by `snr`. `snr` signal to noise ratio to determine `sig`; default value: `5`. `domain` the domain; default value: `c(0,1)`. `delta` the proportion of the domain to be observed for each trajectory; default value: `1`.

## Details

The number of observation for each trajectory is randomly generated by `rpois(m)+1`. For each trajectory, the reference time `Oi` is uniformly sampled from the interval `[domain[1]+delta*L/2,domain[2]-delta*L/2]`, where `L` is the length of `domain`, and the design points for the trajectory is uniformly sampled from the interval `[Oi-delta*L/2,Oi+delta*L/2]`.

## Value

a list with the following members

`t`

list of design points sorted in increasing order for each trajectory.

`y`

list of vectors of observations for each trajectory.

and with attributes `sig`, `snr`, `domain`, `delta` and

y0

`n*m` matrix of observations without measurement errors.

\insertRef

Lin2020synfd

## Examples

 ```1 2 3 4 5 6 7 8``` ```# Gaussian trajectories with constant mean function 1 Y <- irreg.fd(mu=1, X=gaussian.process(), n=10, m=5) # trajectories froma a process defined via K-L representation Y <- irreg.fd(mu=cos, X=kl.process(eigen.functions='FOURIER',distribution='LAPLACE'),n=10, m=5) # trajectories with specified individual sampling rate Y <- irreg.fd(mu=1, X=gaussian.process(cov=matern), n=10, m=rpois(10,3)+2) ```

synfd documentation built on July 1, 2020, 6:04 p.m.