R/Distributions.R

In GAS: Generalized Autoregressive Score Models

DistLabels <- function() {
    return(c("norm",
             "snorm",
             "std",
             "sstd",
             "ast",
             "ast1",
             "ald",
             # "ghskt",
             "poi",
             "ber",
             "gamma",
             "exp",
             "beta",
             "negbin",
             "skellam",
             "mvnorm",
             "mvt"))
}

DistName <- function(DistLabel) {
    if (DistLabel == "norm")
        return("Gaussian")
    if (DistLabel == "snorm")
        return("Skew-Gaussian")
    if (DistLabel == "std")
        return("Student-t")
    if (DistLabel == "sstd")
        return("Skew-Student-t")
    if (DistLabel == "ast")
        return("Asymmetric Student-t with two tail decay parameters")
    if (DistLabel == "ast1")
        return("Asymmetric Student-t with one tail decay parameter")
    if (DistLabel == "ald")
        return("Asymmetric Laplace Distribution")
  if (DistLabel == "ghskt")
    return("Generalized Hyperbolic Skew Student-t Distribution")
    if (DistLabel == "poi")
        return("Poisson")
    if (DistLabel == "ber")
        return("Bernoulli")
    if (DistLabel == "gamma")
        return("Gamma")
    if (DistLabel == "exp")
        return("Exponential")
    if (DistLabel == "beta")
        return("Beta")
  if (DistLabel == "negbin")
    return("Negative Binomial")
  if (DistLabel == "skellam")
    return("Skellam")
    if (DistLabel == "mvnorm")
        return("Multivariate Gaussian")
    if (DistLabel == "mvt")
        return("Multivariate Student-t")
}

DistNote <- function(DistLabel) {
    if (DistLabel == "norm")
        return("")
    if (DistLabel == "snorm")
        return("Skew Gaussian distribution of Fernandez and Steel (1998). It is reparameterized as in
               fGARCH and rugarch such that the location is the mean and the scale is the standard deviation.")
    if (DistLabel == "std")
        return("The Student-t distribution (not reparameterized in terms of the variance parameter)")
    if (DistLabel == "sstd")
        return("This is the Skew-Student-t distribution of Fernandez and Steel (1998). It is reparameterized as in
               fGARCH and rugarch such that the location is the mean and the scale is the standard deviation.")
    if (DistLabel == "ast")
        return("")
    if (DistLabel == "ast1")
        return("Constraint version of ast")
    if (DistLabel == "ald")
        return("The theta, sigma, kappa reparameterisation is used, see Kotz et al. (2001)")
  if (DistLabel == "ghskt")
    return("We use the same implementation of the rugarch package of Ghalanos (2016).")
    if (DistLabel == "poi")
        return("For the Poisson distribution 'location' means the usual intensity parameter")
    if (DistLabel == "ber")
        return("For the Bernoulli distribution 'location' means the probability of success parameter")
    if (DistLabel == "gamma")
        return("")
    if (DistLabel == "beta")
        return("For the Beta distribution 'shape' means the usual alpha parameter and 'scale' means the usual beta parameter")
    if (DistLabel == "exp")
        return("For the Exponential distribution 'location' means the usual rate parameter")
    if (DistLabel == "skellam")
        return("The Skellam distribution reparameterized in terms of mean and variance.")
    if (DistLabel == "negbin")
        return("The negative binomial distribution with size = nu and prob = pi. Both parameters can be time-varying,
                however, only pi can be be used with a scaled score. For the Negative Binomial distribution 'location'
                means the probability of success parameter, and 'scale' refers to the size parameter.")
    if (DistLabel == "mvnorm")
        return("")
    if (DistLabel == "mvt")
        return("")
}

DistReference <- function(DistLabel) {
    if (DistLabel == "norm")
        return("")
    if (DistLabel == "snorm")
        return("Fernandez, Carmen, and Mark FJ Steel. 'On Bayesian modeling of fat tails and skewness.' Journal of the American Statistical Association 93.441 (1998): 359-371.")
    if (DistLabel == "std")
        return("")
    if (DistLabel == "sstd")
        return("Fernandez, Carmen, and Mark FJ Steel. 'On Bayesian modeling of fat tails and skewness.' Journal of the American Statistical Association 93.441 (1998): 359-371.")
    if (DistLabel == "ast")
        return("Zhu, D., & Galbraith, J. W. (2010). A generalized asymmetric Student-t distribution with application to financial econometrics. Journal of Econometrics, 157(2), 297-305.")
    if (DistLabel == "ast1")
        return("Zhu, D., & Galbraith, J. W. (2010). A generalized asymmetric Student-t distribution with application to financial econometrics. Journal of Econometrics, 157(2), 297-305.")
    if (DistLabel == "ald")
        return("Kotz, S., Kozubowski, T., & Podgorski, K. (2001). The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance. Springer Science & Business Media.")
  if (DistLabel == "ghskt")
    return("Aas, K. and Haff, I. H. (2006). The Generalized Hyperbolic Skew Student's t-Distribution. Journal of Financial Econometrics, 4(2), 275-309.")
    if (DistLabel == "poi")
        return("")
    if (DistLabel == "ber")
        return("")
    if (DistLabel == "exp")
        return("")
    if (DistLabel == "beta")
        return("")
    if (DistLabel == "gamma")
        return("")
  if (DistLabel == "negbin")
    return("")
  if (DistLabel == "skellam")
    return("")
    if (DistLabel == "mvnorm")
        return("")
    if (DistLabel == "mvt")
        return("")
}

DistParameters <- function(DistLabel) {
    if (DistLabel == "norm")
        return(c("location", "scale"))
    if (DistLabel == "snorm")
        return(c("location", "scale", "skewness"))
    if (DistLabel == "std")
        return(c("location", "scale", "shape"))
    if (DistLabel == "sstd")
        return(c("location", "scale", "skewness", "shape"))
    if (DistLabel == "ast")
        return(c("location", "scale", "skewness", "shape", "shape2"))
    if (DistLabel == "ast1")
        return(c("location", "scale", "skewness", "shape"))
    if (DistLabel == "ald")
        return(c("location", "scale", "skewness"))
    if (DistLabel == "ghskt")
        return(c("location", "scale", "skewness", "shape"))
    if (DistLabel == "poi")
        return(c("location"))
    if (DistLabel == "ber")
        return(c("location"))
    if (DistLabel == "gamma")
        return(c("scale", "shape"))
    if (DistLabel == "exp")
        return(c("location"))
    if (DistLabel == "beta")
        return(c("scale", "shape"))
    if (DistLabel == "skellam")
        return(c("location", "scale"))
    if (DistLabel == "negbin")
        return(c("location", "scale"))
    if (DistLabel == "mvnorm")
        return(c("location", "scale", "correlation"))
    if (DistLabel == "mvt")
        return(c("location", "scale", "correlation", "shape"))
}

DistType <- function(DistLabel) {
    if (DistLabel == "norm")
        return("univariate")
    if (DistLabel == "snorm")
        return("univariate")
    if (DistLabel == "std")
        return("univariate")
    if (DistLabel == "sstd")
        return("univariate")
    if (DistLabel == "ast")
        return("univariate")
    if (DistLabel == "ast1")
        return("univariate")
    if (DistLabel == "ald")
        return("univariate")
    if (DistLabel == "ghskt")
        return("univariate")
    if (DistLabel == "poi")
        return("univariate")
    if (DistLabel == "ber")
        return("univariate")
    if (DistLabel == "gamma")
        return("univariate")
    if (DistLabel == "exp")
        return("univariate")
    if (DistLabel == "beta")
        return("univariate")
    if (DistLabel == "negbin")
        return("univariate")
    if (DistLabel == "skellam")
        return("univariate")
    if (DistLabel == "mvnorm")
        return("multivariate")
    if (DistLabel == "mvt")
        return("multivariate")
}

DistScalingType <- function(DistLabel) {
    if (DistLabel == "norm")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "snorm")
        return("Identity")
    if (DistLabel == "std")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "sstd")
        return("Identity")
    if (DistLabel == "ast")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "ast1")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "ald")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "ghskt")
        return("Identity")
    if (DistLabel == "poi")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "ber")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "gamma")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "exp")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "beta")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "negbin")
        return("Identity, Inv, InvSqrt")
    if (DistLabel == "skellam")
        return("Identity")
    if (DistLabel == "mvnorm")
        return("Identity")
    if (DistLabel == "mvt")
        return("Identity")
}

DistInfo <- function(DistLabel = NULL, N = 2L, FULL = TRUE) {
    if (is.null(DistLabel))
        DistLabel = DistLabels()
    for (i in 1:length(DistLabel)) {
        cat("\n-------------------------------------------------------")
        cat(paste("\nName:\t", DistName(DistLabel[i]), sep = ""))
        cat(paste("\nLabel:\t", DistLabel[i], sep = ""))
        cat(paste("\nType:\t", DistType(DistLabel[i]), sep = ""))
        cat(paste("\nParameters:\t", paste(DistParameters(DistLabel[i]), collapse = ", "), sep = ""))
        if (DistType(DistLabel[i]) == "univariate")
            cat(paste("\nNumber of Parameters:\t", NumberParameters(DistLabel[i]), sep = ""))
        if (DistType(DistLabel[i]) == "multivariate")
            cat(paste("\nNumber of Parameters:\t", NumberParameters(DistLabel[i], N), " with N = ",
                N, sep = ""))
        if (FULL) {
          cat(paste("\nScaling Type:\t", DistScalingType(DistLabel[i])))
          cat(paste("\nNote:\t", DistNote(DistLabel[i])))
        }
        cat(paste("\nReferences:\t", DistReference(DistLabel[i]), sep = ""))
        cat("\n-------------------------------------------------------")
    }
}