mTSMSN {TSMSN}

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.

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).

Value

Returns the four moments, the skewness (S), kurtosis (k) and coefficient of variation(CV). If “empir = TRUE”, returns also the Empirical moments.

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.

Examples

mTSMSN(mu = 1, sigma2 = 1, nu = NULL, lambda = 1, a = -2, b = 2, dist = "SN", empir = TRUE)