Density function for the skewed t distribution with k degrees of freedom, scale parameter sigma and skewness eta .
dst(x, sigma, k, eta)dst gives the density corresponding to the simga, k and eta values provided.
vector of quantiles.
scale parameter (\(> 0\)).
degrees of freedom (\(> 0\), maybe non-integer). df = Inf is allowed.
skewness parameter (\(> 0\)).
Sergio Venturini sergio.venturini@unicatt.it,
Jessica A. Myers jmyers6@partners.org
This distribution is based on introducing skewing into the symmetric scaled t distribution, as described in Fernandez and Steel (1998).
The parameters characterizing the center (here set at 0) and the spread (sigma) refer to the mean and standard deviation of the underlying symmetric distribution.
In the skewed t distribution, the centrality parameter defines the mode of the distribution, but it is no longer either the mean or the median. Similarly, in the skewed t distribution, sigma still characterizes the spread, but it can no longer be interpreted directly as the standard deviation of the distribution.
Fernandez, C. and Steel, M. (1998), "On Bayesian Modeling of Fat Tails and Skewness". Journal of the American Statistical Association, 93, 359-371.
Lee, K. and Thompson, S. (2008), "Flexible Parametric Models for Random-Effects Distributions". Statistics in Medicine, 27, 418-434.
Myers, J. A., Venturini, S., Dominici, F. and Morlock, L. (2011), "Random Effects Models for Identifying the Most Harmful Medication Errors in a Large, Voluntary Reporting Database". Technical Report.
dt.