Title:	Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions
Version:	1.1-11
Description:	Functions to fit finite mixture of scale mixture of skew-normal (FM-SMSN) distributions, details in Prates, Lachos and Cabral (2013) <doi:10.18637/jss.v054.i12>, Cabral, Lachos and Prates (2012) <doi:10.1016/j.csda.2011.06.026> and Basso, Lachos, Cabral and Ghosh (2010) <doi:10.1016/j.csda.2009.09.031>.
Depends:	R (≥ 1.9.0), mvtnorm (≥ 0.9-9)
Author:	Marcos Prates [aut, cre, trl], Victor Lachos [aut], Celso Cabral [aut]
Maintainer:	Marcos Prates <marcosop@est.ufmg.br>
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2.0)]
Packaged:	2025-04-23 18:00:56 UTC; marcos
Repository:	CRAN
NeedsCompilation:	no
Date/Publication:	2025-04-23 18:30:01 UTC

Body Mass Index

Description

The data set has the measure of the Body Mass Index (bmi) for 2107 people.

Usage

data(bmi)

Format

A data frame with 2107 observations of bmi

Source

Rodrigo M. Basso, Victor H. Lachos, Celso R. B. Cabral, Pulak Ghosh (2009). "Robust mixture modeling based on scale mixtures of skew-normal distributions". Computational Statistics and Data Analysis (in press). doi: 10.1016/j.csda.2009.09.031

References

Marcos Oliveira Prates, Celso Romulo Barbosa Cabral, Victor Hugo Lachos (2013)."mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions". Journal of Statistical Software, 54(12), 1-20., URL https://doi.org/10.18637/jss.v054.i12.

Examples

## Not run: 
data(bmi)
y <-bmi$bmi

hist(y,breaks=40)

## Maximum likelihood estimaton (MLE) with generated values
bmi.analysis <- smsn.mix(y, nu = 3, g = 2, get.init = TRUE, criteria = TRUE, 
                         group = TRUE, calc.im=TRUE)
mix.hist(y,bmi.analysis)

## Passing initial values to MLE
mu1 <- 20; mu2 <- 35
sigma2.1 <- 9; sigma2.2 <- 9;
lambda1 <- 0; lambda2 <- 0;
pii<- c(0.5,0.5)

mu <- c(mu1,mu2)
sigma2 <- c(sigma2.1,sigma2.2)
shape <- c(lambda1,lambda2)

bmi.analysis <- smsn.mix(y, nu = 3, mu, sigma2 , shape, pii, get.init = FALSE,
                         criteria = TRUE, group = TRUE, calc.im=FALSE)
mix.hist(y,bmi.analysis)

## Calculate the information matrix (when the calc.im option in smsn.mix is set FALSE)
bmi.im <-  im.smsn(y, bmi.analysis)

## Search for the best number of clusters from g=1 to g=5
bmi.analysis <- smsn.search(y, nu = 3, g.min = 1, g.max=5)
mix.hist(y,bmi.analysis$best.model)

## End(Not run)

Old Faithful Geyser Data

Description

Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA.

Usage

data(faithful)

Format

A data frame with 272 observations on 2 variables (p=2)

Source

H?rdle, W. (1991) "Smoothing Techniques with Implementation in S". New York: Springer.

Azzalini, A. and Bowman, A. W. (1990). "A look at some data on the Old Faithful geyser". Applied Statistics 39, 357–365.

References

Marcos Oliveira Prates, Celso Romulo Barbosa Cabral, Victor Hugo Lachos (2013)."mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions". Journal of Statistical Software, 54(12), 1-20., URL https://doi.org/10.18637/jss.v054.i12.

Examples

## Not run: 
data(faithful)

## Maximum likelihood estimaton (MLE) for the multivariate FM-SMSN distribution
## with generated values
## Normal
Norm.analysis <- smsn.mmix(faithful, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Normal")
mix.contour(faithful,Norm.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Calculate the information matrix (when the calc.im option in smsn.mmix is set FALSE)
Norm.im <-  imm.smsn(faithful, Norm.analysis)

## Skew-Normal
Snorm.analysis <- smsn.mmix(faithful, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Skew.normal")
mix.contour(faithful,Snorm.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Calculate the information matrix (when the calc.im option in smsn.mmix is set FALSE)
Snorm.im <-  imm.smsn(faithful, Snorm.analysis)

## Skew-t
St.analysis <- smsn.mmix(faithful, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Skew.t")
mix.contour(faithful,St.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Calculate the information matrix (when the calc.im option in smsn.mmix is set FALSE)
St.im <-  imm.smsn(faithful, St.analysis)

## Passing initial values to MLE and automaticaly calculate the information matrix
mu1 <- c(5,77)
Sigma1 <- matrix(c(0.18,0.60,0.60,41), 2,2)
shape1 <- c(0.69,0.64)

mu2 <- c(2,52)
Sigma2 <- matrix(c(0.15,1.15,1.15,40), 2,2)
shape2 <- c(4.3,2.7)

pii<-c(0.65,0.35)

mu <- list(mu1,mu2)
Sigma <- list(Sigma1,Sigma2)
shape <- list(shape1,shape2)

Snorm.analysis <- smsn.mmix(faithful, nu=3, mu=mu, Sigma=Sigma, shape=shape, pii=pii,
                            g=2, get.init = FALSE, group = TRUE,
                            family = "Skew.normal", calc.im=TRUE)
                            
mix.contour(faithful,Snorm.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Search for the best number of clusters from g=1 to g=3
faithful.analysis <- smsn.search(faithful, nu = 3, g.min = 1, g.max=3)
mix.contour(faithful,faithful.analysis$best.model,x.min=1,x.max=1,
            y.min=15,y.max=10,levels = c(0.1, 0.015, 0.005, 0.0009,
            0.00015)) 

## End(Not run)

Information matrix

Description

Calculate the information matrix of returned analysis based on the model family choice (univariate case, p=1).

Usage

im.smsn(y, model)

Arguments

Value

Estimate the Information Matrix of the parameters.

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

See Also

smsn.mix

Examples

 ## see \code{\link{bmi}}

Information matrix

Description

Calculate the information matrix of returned analysis based on the model family choice (multivariate case, p>=2).

Usage

imm.smsn(y, model)

Arguments

Value

Estimate the Information Matrix of the parameters. Note: In the Information Matrix the scale parameters estimates are relative to the entries of square root matrix of Sigma.

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

See Also

smsn.mmix

Examples

 ## see \code{\link{faithful}}

Print the selected groups with contours

Description

Plot the contour of the observations with the group selection.

Usage

mix.contour(y, model,
            slice=100, ncontour=10,
            x.min=1, x.max=1,
            y.min=1,y.max=1,
            ...)

Arguments

See Also

smsn.mmix

Examples

 ## see \code{\link{smsn.mmix}}

Estimated densities

Description

Plot the estimated density or log-density (univariate case, p=1).

Usage

mix.dens(y, model, log=FALSE, ylab=NULL, xlab = NULL, main = NULL, ...)

Arguments

See Also

smsn.mix

Examples

 ## see \code{\link{bmi}} and \code{\link{smsn.mix}}

Estimated densities

Description

Plot the histogram along with the estimated density (univariate case, p=1).

Usage

mix.hist(y, model, breaks, main, col.hist, col.dens, ...)

Arguments

See Also

smsn.mix

Examples

 ## see \code{\link{bmi}} and \code{\link{smsn.mix}}

Plot lines of smsn densities

Description

Add lines of smsn estimated denisty or log-density in mix.dens plots (univariate case, p=1).

Usage

mix.lines(y, model, log=FALSE, ...)

Arguments

See Also

smsn.mix

Examples

 ## see \code{\link{bmi}} and \code{\link{smsn.mix}}

Printing mix object

Description

Printing a smsn.mix object (univariate case, p=1)

Usage

mix.print(model, digits = 3, ...)

Arguments

See Also

smsn.mix

Random univariate FM-SMSN generator

Description

Random generator of univariate FM-SMSN distributions.

Usage

rmix(n, pii, family, arg, cluster=FALSE)

Arguments

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

See Also

smsn.mix

Examples

 ## see \code{\link{smsn.mix}}

Random multivariate FM-SMSN generator

Description

Random generator of multivariate FM-SMSN distributions.

Usage

rmmix(n, pii, family, arg, cluster=FALSE)

Arguments

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

See Also

smsn.mmix

Examples

 ## see \code{\link{smsn.mmix}}

Fit univariate FM-SMSN distribution

Description

Return EM algorithm output for FM-SMSN distributions (univaritate case, p=1).

Usage

smsn.mix(y, 
         nu, mu = NULL, sigma2 = NULL, shape = NULL, pii = NULL,
         g = NULL, get.init = TRUE,
         criteria = TRUE, group = FALSE, family = "Skew.normal",
         error = 0.00001, iter.max = 100, calc.im = TRUE, obs.prob = FALSE,
         kmeans.param = NULL)

Arguments

Value

Estimated values of the location, scale, skewness and kurtosis parameter.

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

References

Rodrigo M. Basso, Victor H. Lachos, Celso R. B. Cabral, Pulak Ghosh (2010). "Robust mixture modeling based on scale mixtures of skew-normal distributions". Computational Statistics and Data Analysis, 54, 2926-2941. doi: 10.1016/j.csda.2009.09.031

Marcos Oliveira Prates, Celso Romulo Barbosa Cabral, Victor Hugo Lachos (2013)."mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions". Journal of Statistical Software, 54(12), 1-20., URL https://doi.org/10.18637/jss.v054.i12.

See Also

mix.hist, im.smsn and smsn.search

Examples

mu1 <- 5; mu2 <- 20; mu3 <- 35
sigma2.1 <- 9; sigma2.2 <- 16; sigma2.3 <- 9
lambda1 <- 5; lambda2 <- -3; lambda3 <- -6
nu = 5

mu <- c(mu1,mu2,mu3)
sigma2 <- c(sigma2.1,sigma2.2,sigma2.3)
shape <- c(lambda1,lambda2,lambda3)
pii <- c(0.5,0.2,0.3)

arg1 = c(mu1, sigma2.1, lambda1, nu)
arg2 = c(mu2, sigma2.2, lambda2, nu)
arg3 = c(mu3, sigma2.3, lambda3, nu)
y <- rmix(n=1000, p=pii, family="Skew.t", arg=list(arg1,arg2,arg3))

## Not run: 
par(mfrow=c(1,2))
## Normal fit
Norm.analysis <- smsn.mix(y, nu = 3, g = 3, get.init = TRUE, criteria = TRUE, 
                          group = TRUE, family = "Normal", calc.im=FALSE)
mix.hist(y,Norm.analysis)
mix.print(Norm.analysis)
mix.dens(y,Norm.analysis)

## Skew Normal fit
Snorm.analysis <- smsn.mix(y, nu = 3, g = 3, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Skew.normal", calc.im=FALSE)
mix.hist(y,Snorm.analysis)
mix.print(Snorm.analysis)
mix.dens(y,Snorm.analysis)

## t fit
t.analysis <- smsn.mix(y, nu = 3, g = 3, get.init = TRUE, criteria = TRUE, 
                        group = TRUE, family = "t", calc.im=FALSE)
mix.hist(y,t.analysis)
mix.print(t.analysis)
mix.dens(y,t.analysis)

## Skew t fit
St.analysis <- smsn.mix(y, nu = 3, g = 3, get.init = TRUE, criteria = TRUE, 
                        group = TRUE, family = "Skew.t", calc.im=FALSE)
mix.hist(y,St.analysis)
mix.print(St.analysis)
mix.dens(y,St.analysis)

## Skew Contaminated Normal fit
Scn.analysis <- smsn.mix(y, nu = c(0.3,0.3), g = 3, get.init = TRUE, criteria = TRUE, 
                         group = TRUE, family = "Skew.cn", calc.im=FALSE)
mix.hist(y,Scn.analysis)
mix.print(Scn.analysis)
mix.dens(y,Scn.analysis)

par(mfrow=c(1,1))
mix.dens(y,Norm.analysis)
mix.lines(y,Snorm.analysis,col="green")
mix.lines(y,t.analysis,col="red")
mix.lines(y,St.analysis,col="blue")
mix.lines(y,Scn.analysis,col="grey")

## End(Not run)

Fit multivariate FM-SMSN distributions.

Description

Return EM algorithm output for multivariate FM-SMSN distributions.

Usage

smsn.mmix(y, nu=1,
          mu = NULL, Sigma = NULL, shape = NULL, pii = NULL,
          g = NULL, get.init = TRUE, criteria = TRUE,
          group = FALSE, family = "Skew.normal", 
          error = 0.0001, iter.max = 100, uni.Gama = FALSE,
          calc.im=FALSE, obs.prob = FALSE, kmeans.param = NULL)

Arguments

Value

Estimated values of the location, scale, skewness and kurtosis parameter. Note: The scale parameters estimated are relative to the entries of the squae root matrix of Sigma.

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

References

Cabral, C. R. B., Lachos, V. H. and Prates, M. O. (2012). "Multivariate Mixture Modeling Using Skew-Normal Independent Distributions". Computational Statistics & Data Analysis, 56, 126-142, doi:10.1016/j.csda.2011.06.026.

Marcos Oliveira Prates, Celso Romulo Barbosa Cabral, Victor Hugo Lachos (2013)."mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions". Journal of Statistical Software, 54(12), 1-20., URL https://doi.org/10.18637/jss.v054.i12.

See Also

mix.contour, rmmix and smsn.search

Examples

mu1 <- c(0,0)
Sigma1 <- matrix(c(3,1,1,3), 2,2)
shape1 <-c(4,4)
nu1 <- 4

mu2 <- c(5,5)
Sigma2 <- matrix(c(2,1,1,2), 2,2)
shape2 <-c(2,2)
nu2 <- 4

pii<-c(0.6,0.4)

arg1 = list(mu=mu1, Sigma=Sigma1, shape=shape1, nu=nu1)
arg2 = list(mu=mu2, Sigma=Sigma2, shape=shape2, nu=nu2)
y <- rmmix(n= 500, p = pii, "Skew.t", list(arg1,arg2))

## Not run: 

## Normal fit giving intial values
mu <- list(mu1,mu2)
Sigma <- list(Sigma1,Sigma2)
shape <- list(shape1,shape2)
pii <- c(0.6,0.4)

Norm.analysis <- smsn.mmix(y, nu=3, mu=mu, Sigma=Sigma, shape=shape, pii = pii,
                           criteria = TRUE, g=2, get.init = FALSE, group = TRUE,
                           family = "Normal")
mix.contour(y,Norm.analysis)

## Normal fit 
Norm.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Normal")
mix.contour(y,Norm.analysis)

## Normal fit with a unique Gamma
Norm.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Normal", uni.Gama = TRUE)
mix.contour(y,Norm.analysis)


## Skew Normal fit
Snorm.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                            group = TRUE, family = "Skew.normal")
mix.contour(y,Snorm.analysis)

## t fit
t.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                         group = TRUE, family = "t")
mix.contour(y,t.analysis)

## Skew t fit
St.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                         group = TRUE, family = "Skew.t")
mix.contour(y,St.analysis)

## Skew Contaminated Normal fit
Scn.analysis <- smsn.mmix(y, nu=c(0.1,0.1), g=2, get.init = TRUE, criteria = TRUE, 
                          group = TRUE, family = "Skew.cn",error=0.01)
mix.contour(y,Scn.analysis)

## Skew Contaminated Normal fit
Sslash.analysis <- smsn.mmix(y, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                             group = TRUE, family = "Skew.slash", error=0.1)
mix.contour(y,Sslash.analysis)


## End(Not run)

Find the best number of cluster for a determined data set.

Description

Search for the best fitting for number of cluster from g.min to g.max for a selected family and criteria for both univariate and multivariate distributions.

Usage

smsn.search(y, nu,
            g.min = 1, g.max = 3,
            family = "Skew.normal", criteria = "bic",
            error = 0.0001, iter.max = 100, 
            calc.im = FALSE, uni.Gama = FALSE, kmeans.param = NULL, ...)

Arguments

Value

Estimated values of the location, scale, skewness and kurtosis parameter from the optimum number of clusters.

Author(s)

Marcos Prates marcosop@est.ufmg.br, Victor Lachos hlachos@ime.unicamp.br and Celso Cabral celsoromulo@gmail.com

See Also

smsn.mix and smsn.mmix

Examples

 ## see \code{\link{bmi}} and \code{\link{faithful}}