This data set was simulated from all families of distributions
available in unitquantreg package considering
the median, i.e., \(\tau=0.5\).
Usage
data(sim_bounded, package = "unitquantreg")Format
data.frame with 1300 observations and 5 columns:
y1: simulated response variable with constant shape parameter, \(\theta = 2\).y2: simulated response variable with regression structure in the shape parameter, \(\theta_i = \exp(\zeta_i\)), where \(\zeta_i = \mathbf{z}_i^\top\,\boldsymbol{\gamma}\).x: covariate related to \(\mu_i\), i.e., the median.z: covariate related to \(\theta_i\), i.e., the shape parameter.family: string indicating the family of distribution.
Details
There are two response variable, namely y1 and y2.
The former was simulated considering a regression structure for
\(\mu\) and one covariate simulated from a standard uniform distribution,
where the true vector of coefficients for \(\mu\) is
\(\boldsymbol{\beta} = (1, 2)\) and \(\theta = 2\).
The latter was simulated assuming a regression structure for both \(\mu\)
and \(\theta\) (shape parameter) and only one independent covariates
simulated from two standard uniform distributions. The true vectors of
coefficients for \(\mu\) and \(\theta\) are
\(\boldsymbol{\beta} = (1, 2)\) and \(\boldsymbol{\gamma} = (-1, 1)\),
respectively.