Title: Truncated Scale Mixtures of Skew-Normal Distributions
Version: 0.0.1
Description: Return the first four moments, estimation of parameters and sample of the TSMSN distributions (Skew Normal, Skew t, Skew Slash or Skew Contaminated Normal).
License: MIT + file LICENSE
Encoding: UTF-8
LazyData: true
Imports: sn, mvtnorm, numDeriv, progress
RoxygenNote: 6.1.1
NeedsCompilation: no
Packaged: 2019-07-02 23:16:05 UTC; eraldofilho
Author: Eraldo B. dos Anjos Filho ORCID iD [aut, cre], Aldo M. Garay ORCID iD [aut]
Maintainer: Eraldo B. dos Anjos Filho <ebdaf1@de.ufpe.br>
Repository: CRAN
Date/Publication: 2019-07-04 07:40:03 UTC

TSMSN: Truncated Scale Mixtures of Skew-Normal Distributions

Description

Return the first four moments, estimation of parameters and sample of the TSMSN distributions (Skew Normal, Skew t, Skew Slash or Skew Contaminated Normal).

Author(s)

Maintainer: Eraldo B. dos Anjos Filho ebdaf1@de.ufpe.br (0000-0002-1272-2794)

Authors:

Estimate the parameters of Truncated Scale Mixtures of Skew-Normal Distributions

Description

This function obtains the maximum likelihood estimators of the TSMSN (Skew-Normal, Skew-t, Skew-Slash and Skew-Contaminated Normal) distribution parameters by direct maximization.

Usage

eTSMSN(x, mu = 0.01, sigma2 = 1.01, lambda = 0, nu = 5, a = -Inf,
  b = Inf, dist = "SN", shape = FALSE)

Arguments

x

Dataset.

mu

Initial location parameter (Optional).

sigma2

Initial scale parameter (Optional).

lambda

Initial skewness parameter (Optional).

nu

Fixed 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.

shape

For ST, SSL and SCN distribution. Consider the parameter nu as fixed and known. If TRUE nu must be provided.

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). For the estimation in the cases of distributions ST, SSL and SCN nu is considered fixed, but may be known or unknown. The shape parameter is the one that regulates if nu is known or unknown.

Value

Returns a vector with the maximum likelihood estimators of the distribution parameters.

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

x <- rTSMSN(n = 100, mu = 0, sigma2 = 1, lambda = 0, nu = NULL, a = -2, b = 2, dist = "SN")
eTSMSN(x, a = -2, b = 2, dist = "SN")

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)

Generate the Truncated Scale Mixtures of Skew-Normal Distributions

Description

This function generate random samples from Skew-Normal, Skew-t, Skew-Slash and Skew-Contaminated Normal, using the the inverse method.

Usage

rTSMSN(n, mu = 0, sigma2 = 1, lambda = 0, nu = NULL, a = -Inf,
  b = Inf, dist = "SN")

Arguments

n

Number of observations.

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.

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 a vector with the sample generated according to the distribution and parameters defined.

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

rTSMSN(n = 100, mu = 0, sigma2 = 1, nu = NULL, lambda = 0, a = -Inf, b = Inf, dist = "SN")

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