# lol.sims.fat_tails: Fat Tails Simulation In lolR: Linear Optimal Low-Rank Projection

## Description

A function for simulating from 2 classes with differing means each with 2 sub-clusters, where one sub-cluster has a narrow tail and the other sub-cluster has a fat tail.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```lol.sims.fat_tails( n, d, rotate = FALSE, f = 15, s0 = 10, rho = 0.2, t = 0.8, priors = NULL ) ```

## Arguments

 `n` the number of samples of the simulated data. `d` the dimensionality of the simulated data. `rotate` whether to apply a random rotation to the mean and covariance. With random rotataion matrix `Q`, `mu = Q*mu`, and `S = Q*S*Q`. Defaults to `FALSE`. `f` the fatness scaling of the tail. S2 = f*S1, where S1_ij = rho if i != j, and 1 if i == j. Defaults to `15`. `s0` the number of dimensions with a difference in the means. s0 should be < d. Defaults to `10`. `rho` the scaling of the off-diagonal covariance terms, should be < 1. Defaults to `0.2`. `t` the fraction of each class from the narrower-tailed distribution. Defaults to `0.8`. `priors` the priors for each class. If `NULL`, class priors are all equal. If not null, should be `|priors| = K`, a length `K` vector for `K` classes. Defaults to `NULL`.

## Value

A list of class `simulation` with the following:

 `X` `[n, d]` the `n` data points in `d` dimensions as a matrix. `Y` `[n]` the `n` labels as an array. `mus` `[d, K]` the `K` class means in `d` dimensions. `Sigmas` `[d, d, K]` the `K` class covariance matrices in `d` dimensions. `priors` `[K]` the priors for each of the `K` classes. `simtype` The name of the simulation. `params` Any extraneous parameters the simulation was created with.

## Details

For more details see the help vignette: `vignette("sims", package = "lolR")`

Eric Bridgeford

## Examples

 ```1 2 3``` ```library(lolR) data <- lol.sims.fat_tails(n=200, d=30) # 200 examples of 30 dimensions X <- data\$X; Y <- data\$Y ```

lolR documentation built on July 8, 2020, 7:35 p.m.