mTSMSN: Moments of Truncated Scale Mixtures of Skew-Normal Distributions
Description
Return the first four moments of the TSMSN distributions (Skew Normal, Skew t, Skew Slash or Skew Contaminated Normal).
Usage
mTSMSN(mu = 0, sigma2 = 1, lambda = 0, nu = NULL, a = -Inf,
b = Inf, dist = "SN", empir = TRUE)
Arguments
mu
Location parameter.
sigma2
Scale parameter.
lambda
Skewness parameter.
nu
Shape parameter. Must be NULL in case of Skew-Normal distribution. Must be a bidimensional vector in case of skew-contaminated normal distribution (SCN) and contaminated normal distribution (CN).
a
Lower bound.
b
Upper bound.
dist
Distribution to be used: "SN" for Skew-Normal model, "ST" for Skew-t model, "SSL" for Skew-slash model and "SCN" for Skew-contaminated Normal model.
empir
If TRUE provides the empirical moments.
Value
Returns the four moments, the skewness (S), kurtosis (k) and coefficient of variation(CV). If <U+201C>empir = TRUE<U+201D>, returns also the Empirical moments.
Details
For the SMN family, consider lambda = 0. For the Skew-contaminated Normal and Contaminated Normal distribution, each component of the bidimensional vector "nu" must be on (0,1).
References
Lachos, V. H.; Garay, A. M.; Cabral, C. R. "Moments of truncated scale mixtures of skew-normal distributions." Brazilian Journal of Probability and Statistics (In press).
Basso, Rodrigo M., et al. "Robust mixture modeling based on scale mixtures of skew-normal distributions." Computational Statistics & Data Analysis 54.12 (2010): 2926-2941.