simulation_model6: Convenience function for generating functional data

In fdaoutlier: Outlier Detection Tools for Functional Data Analysis

Convenience function for generating functional data

Description

This models generates shape outliers that have a different shape for a portion of the domain. The main model is of the form:

X_i(t) = \mu t + e_i(t),

with contamination model of the form:

X_i(t) = \mu t + (-1)^u q + (-1)^{(1-u)}(\frac{1}{\sqrt{r\pi}})\exp(-z(t-v)^w) + e_i(t)

where: t\in [0,1], e_i(t) is a Gaussian process with zero mean and covariance function of the form:

\gamma(s,t) = \alpha\exp(-\beta|t-s|^\nu),

u follows Bernoulli distribution with probability P(u = 1) = 0.5; q, r, z and w are constants, and v follows a Uniform distribution between an interval [a, b] and m is a constant. Please see the simulation models vignette with vignette("simulation_models", package = "fdaoutlier") for more details.

Usage

simulation_model6(
  n = 100,
  p = 50,
  outlier_rate = 0.1,
  mu = 4,
  q = 1.8,
  kprob = 0.5,
  a = 0.25,
  b = 0.75,
  cov_alpha = 1,
  cov_beta = 1,
  cov_nu = 1,
  pi_coeff = 0.02,
  exp_pow = 2,
  exp_coeff = 50,
  deterministic = TRUE,
  seed = NULL,
  plot = F,
  plot_title = "Simulation Model 6",
  title_cex = 1.5,
  show_legend = T,
  ylabel = "",
  xlabel = "gridpoints"
)

Arguments

n	The number of curves to generate. Set to 100 by default.
p	The number of evaluation points of the curves. Curves are usually generated over the interval [0, 1]. Set to 50 by default.
outlier_rate	A value between [0, 1] indicating the percentage of outliers. A value of 0.06 indicates about 6\% of the observations will be outliers depending on whether the parameter deterministic is TRUE or not. Set to 0.05 by default.
mu	The mean value of the functions in the main and contamination model. Set to 4 by default.
q	The constant term q in the contamination model. Set to 1.8 by default.
kprob	The probability P(u = 1). Set to 0.5 by default.
a, b	Values specifying the interval of from which v in the contamination model is drawn. Set to 0.25 and 0.75 respectively.
cov_alpha	A value indicating the coefficient of the exponential function of the covariance matrix, i.e., the \alpha in the covariance function. Set to 1 by default.
cov_beta	A value indicating the coefficient of the terms inside the exponential function of the covariance matrix, i.e., the \beta in the covariance function. Set to 1 by default.
cov_nu	A value indicating the power to which to raise the terms inside the exponential function of the covariance matrix, i.e., the \nu in the covariance function. Set to 1 by default.
pi_coeff	The constant r in the contamination model i.e., the coefficient of of pi. Set to 0.02 by default.
exp_pow	The constant w in the contamination model i.e., the power of the term in the exponential function of the contamination model. Set to 2.
exp_coeff	The constant z in the contamination model i.e., the coefficient term in the exponential function of the contamination model. Set to 50 by default.
deterministic	A logical value. If TRUE, the function will always return round(n*outlier_rate) outliers and consequently the number of outliers is always constant. If FALSE, the number of outliers are determined using n Bernoulli trials with probability outlier_rate, and consequently the number of outliers returned is random. TRUE by default.
seed	A seed to set for reproducibility. NULL by default in which case a seed is not set.
plot	A logical value indicating whether to plot data.
plot_title	Title of plot if plot is TRUE
title_cex	Numerical value indicating the size of the plot title relative to the device default. Set to 1.5 by default. Ignored if plot = FALSE.
show_legend	A logical indicating whether to add legend to plot if plot = TRUE.
ylabel	The label of the y-axis. Set to "" by default.
xlabel	The label of the x-axis if plot = TRUE. Set to "gridpoints" by default.

Value

A list containing:

data	a matrix of size n by p containing the simulated data set
true_outliers	a vector of integers indicating the row index of the outliers in the generated data.

Examples

dt <- simulation_model6(n = 50, plot = TRUE)
dim(dt$data)
dt$true_outliers

fdaoutlier documentation built on Oct. 1, 2023, 1:06 a.m.