I don’t remember why I thought I may need this distribution (see Financial Data and the Skewed Generalized T Distribution on JSTOR ) but if you ever need it, here it is
/** @addtogroup skew_generalized_t Skew Generalized T distribution functions
*
* From the sgt R package
* Carter Davis (2015). sgt: Skewed Generalized T Distribution Tree. R package version 2.0.
* https://CRAN.R-project.org/package=sgt
*
* The Skewed Generalized T Distribution is a univariate 5-parameter distribution introuced
* by Theodossiou (1998) and known for its extreme flexibility. Special and limiting cases of
* the SGT distribution include the skewed generalized error distribution, the generalized t
* distribution introduced by McDonald and Newey (1988), the skewed t proposed by Hansen (1994),
* the skewed Laplace distribution, the generalized error distribution (also known as the
* generalized normal distribution), the skewed normal distribution, the student t distribution,
* the skewed Cauchy distribution, the Laplace distribution, the uniform distribution, the
* normal distribution, and the Cauchy distribution.
*
* Hansen, B. E., 1994, Autoregressive Conditional Density Estimation, International Economic
* Review 35, 705-730.
*
* Hansen, C., J. B. McDonald, and W. K. Newey, 2010, Enstrumental Variables Estimation with
* Flexible Distribution sigma Journal of Business and Economic Statistics 28, 13-25.
show original
And an example at
functions {
#include skew_generalized_t.stan
}
data {
int N;
vector[N] x;
}
parameters {
real mu;
real<lower=0> sigma;
real<lower=-1, upper=1> lambda;
real<lower=0> p;
real<lower=0> q;
}
model {
mu ~ normal(0, 4);
sigma ~ exponential(1);
lambda ~ std_normal();
p ~ normal(2, 1);
q ~ normal(7, 2);
show original
With the corresponding R code at
library(sgt)
library(cmdstanr)
# SINGLE VARIABLE ESTIMATION:
### generate random variable
set.seed(7900)
n <- 1000
x <- rsgt(n, mu = 2, sigma = 2, lambda = -0.25, p = 1.7, q = 7)
### Get starting values and estimate the parameter values
start <- list(mu = 0, sigma = 1, lambda = 0, p = 2, q = 10)
result <- sgt.mle(X.f = ~ x, start = start, method = "nlminb")
print(result)
print(summary(result))
fp <- file.path("examples/distribution/stan/skew_generalized_t_example.stan")
mod <- cmdstan_model(fp, include_paths = "./functions/distribution")
mod_skew_gen_t <- mod$sample(
data = list(N = n,
x = x),
show original
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Yes it does. I updated everything for ‘.stanfunctions’ functionality. This also means you have to rename to ‘.stan’ file if you want to use it or check out the dev version of stanc3. My intention is to release the repo once the next version of Stan is out with all these capabilities in. Until then, expect things to possibly break on current or past releases of Stan.
/** @addtogroup skew_generalized_t Skew Generalized T distribution functions
*
* From the sgt R package
* Carter Davis (2015). sgt: Skewed Generalized T Distribution Tree. R package version 2.0.
* https://CRAN.R-project.org/package=sgt
*
* The Skewed Generalized T Distribution is a univariate 5-parameter distribution introuced
* by Theodossiou (1998) and known for its extreme flexibility. Special and limiting cases of
* the SGT distribution include the skewed generalized error distribution, the generalized t
* distribution introduced by McDonald and Newey (1988), the skewed t proposed by Hansen (1994),
* the skewed Laplace distribution, the generalized error distribution (also known as the
* generalized normal distribution), the skewed normal distribution, the student t distribution,
* the skewed Cauchy distribution, the Laplace distribution, the uniform distribution, the
* normal distribution, and the Cauchy distribution.
*
* Hansen, B. E., 1994, Autoregressive Conditional Density Estimation, International Economic
* Review 35, 705-730.
*
* Hansen, C., J. B. McDonald, and W. K. Newey, 2010, Enstrumental Variables Estimation with
* Flexible Distribution sigma Journal of Business and Economic Statistics 28, 13-25.
show original
2 Likes