mixsmsn (version 1.1-10)

smsn.mix: 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

y

the response vector

nu

the parameter of the scale variable (vector or scalar) of the SMSN family (kurtosis parameter). It is necessary to all distributions. For the "Skew.cn" must be a vector of length 2 and values in (0,1)

mu

the vector of initial values (dimension g) for the location parameters

sigma2

the vector of initial values (dimension g) for the scale parameters

shape

the vector of initial values (dimension g) for the skewness parameters

pii

the vector of initial values (dimension g) for the weights for each cluster. Must sum one!

g

the number of cluster to be considered in fitting

get.init

if TRUE, the initial values are generated via k-means

criteria

if TRUE, AIC, DIC, EDC and ICL will be calculated

group

if TRUE, the vector with the classification of the response is returned

family

distribution family to be used in fitting ("Skew.t", "t", "Skew.cn", "Skew.slash", "slash", "Skew.normal", "Normal")

error

the covergence maximum error

iter.max

the maximum number of iterations of the EM algorithm. Default = 100

calc.im

if TRUE, the information matrix is calculated and the standard errors are reported

obs.prob

if TRUE, the posterior probability of each observation belonging to one of the g groups is reported

kmeans.param

a list with alternative parameters for the kmeans function when generating initial values, list(iter.max = 10, n.start = 1, algorithm = "Hartigan-Wong")

Value

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

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

# NOT RUN {
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")
# }