Adjusted Rand Index.

Description

Compares two classifications using the adjusted Rand index (ARI).

Usage

ARI(x=NULL, y=NULL)

Arguments

Details

The ARI has expected value 0 in case of random partition, it is equal to one in case of perfect agreement..

Value

The adjusted Rand index value

Author(s)

Cristina Tortora Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

L. Hubert and P. Arabie (1985) Comparing Partitions, Journal of the Classification 2:193-218.

Examples

##loading banknote data
data(banknote)

##model estimation
res=MGHD(data=banknote[,2:7],  G=2   )

#result
ARI(res@map, banknote[,1])

Discriminant analysis using the mixture of generalized hyperbolic distributions.

Description

Carries out model-based discriminant analysis using 5 different models: the mixture of multiple scaled generalized hyperbolic distributions (MGHD), the mixture of generalized hyperbolic factor analyzers (MGHFA), the mixture of multiple scaled generalized hyperbolic distributions (MSGHD),the mixture of convex multiple scaled generalized hyperbolic distributions (cMSGHD) and the mixture of coaelesed generalized hyperbolic distributions (MCGHD).

Usage

DA(train,trainL,test,testL,method="MGHD",starting="km",max.iter=100,
	eps=1e-2,q=2,scale=TRUE)

Arguments

Value

A list with components

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

R.P. Browne, and P.D. McNicholas (2015). A Mixture of Generalized Hyperbolic Distributions. Canadian Journal of Statistics, 43.2 176-198.
C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification (to appear).
C.Tortora, P.D. McNicholas, and R.P. Browne (2016). Mixtures of Generalized Hyperbolic Factor Analyzers. Advanced in data analysis and classification 10(4) p.423-440.

See Also

"MixGHD" MGHD MGHFA MSGHD cMSGHD MCGHD ARI MixGHD-class MixGHD

Examples

##loading banknote data
data(banknote)
banknote[,1]=as.numeric(factor(banknote[,1]))


##divide the data in training set and test set
train=banknote[c(1:74,126:200),]
test=banknote[75:125,]

##model estimation
 model=DA(train[,2:7],train[,1],test[,2:7],test[,1],method="MGHD",max.iter=20)

#result
model$ARItest

Mixture of coalesced generalized hyperbolic distributions (MCGHD).

Description

Carries out model-based clustering using the mixture of coalesced generalized hyperbolic distributions.

Usage

MCGHD(data=NULL,gpar0=NULL,G=2,max.iter=100,eps=1e-2,label=NULL,
	method="km",scale=TRUE,nr=10, modelSel="AIC")

Arguments

Details

The arguments gpar0, if specified, has to be a list structure containing as much element as the number of components G. Each element must include the following parameters: one p dimensional vector mu, alpha and phi, a pxp matrix gamma, a px2 vector cpl containing the vectors omega and lambda, and a 2-dimensional vector containing the omega0 and lambda0.

Value

A S4 object of class MixGHD with slots:

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification 36(1) 26-57.\ C. Tortora, R. P. Browne, A. ElSherbiny, B. C. Franczak, and P. D. McNicholas (2021). Model-Based Clustering, Classification, and Discriminant Analysis using the Generalized Hyperbolic Distribution: MixGHD R package, Journal of Statistical Software 98(3) 1–24, <doi:10.18637/jss.v098.i03>.

See Also

MGHD, MSGHD

Examples

##loading banknote data
data(banknote)

##model estimation
model=MCGHD(banknote[,2:7],G=2,max.iter=20)

#result
#summary(model)
#plot(model)
table(banknote[,1],model@map)

Mixture of generalized hyperbolic distributions (MGHD).

Description

Carries out model-based clustering and classification using the mixture of generalized hyperbolic distributions.

Usage

MGHD(data=NULL,gpar0=NULL,G=2,max.iter=100,label=NULL,eps=1e-2,
method="kmeans",scale=TRUE,nr=10, modelSel="AIC")

Arguments

Details

The arguments gpar0, if specified, is a list structure containing at least one p dimensional vector mu, and alpha, a pxp matrix sigma, and a 2 dimensional vector containing omega and lambda.

Value

A S4 object of class MixGHD with slots:

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

R.P. Browne, and P.D. McNicholas (2015). A Mixture of Generalized Hyperbolic Distributions. Canadian Journal of Statistics, 43.2 176-198\ C. Tortora, R. P. Browne, A. ElSherbiny, B. C. Franczak, and P. D. McNicholas (2021). Model-Based Clustering, Classification, and Discriminant Analysis using the Generalized Hyperbolic Distribution: MixGHD R package, Journal of Statistical Software 98(3) 1–24, <doi:10.18637/jss.v098.i03>.

Examples

##loading crabs data
data(crabs)

##model estimation
model=MGHD(data=crabs[,4:8],  G=2   )

#result
plot(model)
table(model@map, crabs[,2])

## Classification
##loading bankruptcy data
data(bankruptcy)
#70% belong to the training set
 label=bankruptcy[,1]
#for a Classification porpuse the label cannot be 0
 label[1:33]=2
 a=round(runif(20)*65+1)
 label[a]=0
 
 
##model estimation
model=MGHD(data=bankruptcy[,2:3],  G=2, label=label )

#result
table(model@map,bankruptcy[,1])
plot(model)

Mixture of generalized hyperbolic factor analyzers (MGHFA).

Description

Carries out model-based clustering and classification using the mixture of generalized hyperbolic factor analyzers.

Usage

MGHFA(data=NULL, gpar0=NULL, G=2, max.iter=100, 
label =NULL  ,q=2,eps=1e-2 , method="kmeans", scale=TRUE ,nr=10)

Arguments

Details

The arguments gpar0, if specified, is a list structure containing at least one p dimensional vector mu, alpha and phi, a pxp matrix gamma, a 2 dimensional vector cpl containing omega and lambda.

Value

A S4 object of class MixGHD with slots:

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C.Tortora, P.D. McNicholas, and R.P. Browne (2016). Mixtures of Generalized Hyperbolic Factor Analyzers. Advanced in data analysis and classification 10(4) p.423-440.\ C. Tortora, R. P. Browne, A. ElSherbiny, B. C. Franczak, and P. D. McNicholas (2021). Model-Based Clustering, Classification, and Discriminant Analysis using the Generalized Hyperbolic Distribution: MixGHD R package, Journal of Statistical Software 98(3) 1–24, <doi:10.18637/jss.v098.i03>.

Examples

## Classification
#70% belong to the training set
data(sonar)
 label=sonar[,61]
 set.seed(4)
 a=round(runif(62)*207+1)
 label[a]=0
 
 
##model estimation
model=MGHFA(data=sonar[,1:60],  G=2, max.iter=25  ,q=2,label=label)

#result
table(model@map,sonar[,61])
summary(model)

Mixture of multiple scaled generalized hyperbolic distributions (MSGHD).

Description

Carries out model-based clustering using the mixture of multiple scaled generalized hyperbolic distributions.

Usage

MSGHD(data=NULL,gpar0=NULL,G=2,max.iter=100,label=NULL,eps=1e-2,
	method="km",scale=TRUE,nr=10, modelSel="AIC")

Arguments

Details

The arguments gpar0, if specified, is a list structure containing at least one p dimensional vector mu, alpha and phi, a pxp matrix gamma, and a px2 matrix cpl containing the vector omega and the vector lambda.

Value

A S4 object of class MixGHD with slots:

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification 36(1) 26-57.\ C. Tortora, R. P. Browne, A. ElSherbiny, B. C. Franczak, and P. D. McNicholas (2021). Model-Based Clustering, Classification, and Discriminant Analysis using the Generalized Hyperbolic Distribution: MixGHD R package, Journal of Statistical Software 98(3) 1–24, <doi:10.18637/jss.v098.i03>.

See Also

MGHD

Examples

##loading banknote data
data(banknote)


##model estimation
model=MSGHD(banknote[,2:7],G=2,max.iter=30)

#result
table(banknote[,1],model@map)
summary(model)
plot(model)

Class "MixGHD"

Description

This class pertains to results of the application of function MGHD, MSGHD, cMSGHD, MCGHD, and MGHFA.

Objects from the Class

Objects can be created as a result to a call to MGHD, MSGHD, cMSGHD, MCGHD, and MGHFA.

Slots

index

Value of the index used for model selection (AIC or ICL or BIC or AIC3) for each G,the index used is specified by the user, if not specified AIC is used.

BIC

Bayesian information criterion value.

ICL

ICL index.

AIC

AIC index.

AIC3

AIC3 index.

gpar

A list of the model parameters (in the rotated space for MCGHD).

loglik

The log-likelihood values.

map

A vector of integers indicating the maximum a posteriori classifications for the best model.

par

Only for MCGHD. A list of the model parameters.

z

A matrix giving the raw values upon which map is based.

Methods

plot

signature(x = "MixGHD") Provides plots of MixGHD-class by plotting the following elements:

• the value of the log likelihood for each iteration.

• Scatterplot of the data of all the possible couples of coordinates coloured according to the cluster. Only for less than 10 variables.

• If the number of variables is two: scatterplot and contour plot of the data coloured according to the cluster

summary

summary(x = "MixGHD").

Provides a summary of MixGHD-class objects by printing the following elements:

• The number components used for the model

• BIC;

• AIC;

• AIC3;

• ICL;

• A table with the number of element in each cluster.

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

See Also

MixGHD-class

Examples

##loading bankruptcy data
data(bankruptcy)

##model estimation
#res=MCGHD(data=bankruptcy[,2:3],G=2,method="kmedoids",max.iter=30)
#result
#plot(res)
#summary(res)

Class MixGHD.

Description

This class pertains to results of the application of function MGHD,MCGHD,MSGHD,cMSGHD.

Details

Plot the loglikhelyhood vale for each iteration of the EM algorithm. If p=2 it shows a contour plot. If 2<p<10 shows a splom of the data colored according to the cluster membership.

Slots

Index

Bayesian information criterion value for each combination of G and q.

BIC

Bayesian information criterion value.

gpar

A list of the model parameters.

loglik

The log-likelihood values.

map

A vector of integers indicating the maximum a posteriori classifications for the best model.

z

A matrix giving the raw values upon which map is based.

method

A string indicating the used method: MGHD, MGHFA, MSGHD, cMSGHD, MCGHD.

data

A matrix or data frame such that rows correspond to observations and columns correspond to variables.

par

(only for MCGHD)A list of the model parameters in the rotated space.

Methods

signature(x = "MixGHD", y = "missing")

S4 method for plotting objects of MixGHD-class.

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

See Also

MixGHD-class,MGHD,MCGHD,MSGHD,cMSGHD,MGHFA

Examples

##loading banknote data
data(bankruptcy)


##model estimation
model=MSGHD(bankruptcy[,2:3],G=2,max.iter=30)

#result
summary(model)
plot(model)

Swiss Banknote data

Description

The data set contain 6 measures of 100 genuine and 100 counterfeit Swiss franc banknotes.

Usage

data(banknote)

Format

A data frame with the following variables:

Status

the status of the banknote: genuine or counterfeit

Length

Length of bill (mm)

Left

Width of left edge (mm)

Right

Width of right edge (mm)

Bottom

Bottom margin width (mm)

Top

Top margin width (mm)

Diagonal

Length of diagonal (mm)

References

Flury, B. and Riedwyl, H. (1988). Multivariate Statistics: A practical approach. London: Chapman & Hall, Tables 1.1 and 1.2, pp. 5-8

Bankruptcy data

Description

The data set contain the ratio of retained earnings (RE) to total assets, and the ratio of earnings before interests and taxes (EBIT) to total assets of 66 American firms recorded in the form of ratios. Half of the selected firms had filed for bankruptcy.

Usage

data(bankruptcy)

Format

A data frame with the following variables:

Y

the status of the firm: 0 bankruptcy or 1 financially sound.

RE

ratio

EBIT

ratio

References

Altman E.I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J Finance 23(4): 589-609

Convex mixture of multiple scaled generalized hyperbolic distributions (cMSGHD).

Description

Carries out model-based clustering using the convex mixture of multiple scaled generalized hyperbolic distributions. The cMSGHD only allows conves level sets.

Usage

cMSGHD(data=NULL,gpar0=NULL,G=2,max.iter=100,label=NULL,eps=1e-2,
	method="km",scale=TRUE,nr=10, modelSel="AIC")

Arguments

Details

The arguments gpar0, if specified, is a list structure containing at least one p dimensional vector mu, alpha and phi, a pxp matrix gamma, and a px2 matrix cpl containing the vector omega and the vector lambda.

Value

A S4 object of class MixGHD with slots:

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification 36(1) 26-57.\ C. Tortora, R. P. Browne, A. ElSherbiny, B. C. Franczak, and P. D. McNicholas (2021). Model-Based Clustering, Classification, and Discriminant Analysis using the Generalized Hyperbolic Distribution: MixGHD R package, Journal of Statistical Software 98(3) 1–24, <doi:10.18637/jss.v098.i03>.

See Also

MGHD MSGHD

Examples

##Generate random data
set.seed(3)

mu1 <- mu2 <- c(0,0)
Sigma1 <- matrix(c(1,0.85,0.85,1),2,2)
Sigma2 <- matrix(c(1,-0.85,-0.85,1),2,2)

X1 <- mvrnorm(n=150,mu=mu1,Sigma=Sigma1)
X2 <- mvrnorm(n=150,mu=mu2,Sigma=Sigma2)

X <- rbind(X1,X2)

##model estimation
em=cMSGHD(X,G=2,max.iter=30,method="random",nr=2)



#result
plot(em)

Coefficients for objects of class MixGHD

Description

Coefficents of the estimated model.

Usage

	## S4 method for signature 'MixGHD'
coef(object)

Arguments

Value

The coefficents of the estimated model

Author(s)

Cristina Tortora Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

Examples

##loading bankruptcy data
data(bankruptcy)

##model estimation
res=MCGHD(data=bankruptcy[,2:3],G=2,method="kmedoids",max.iter=30)
#rcoefficients of the model
coef(res)

Contour plot

Description

Contour plot for a given set of parameters.

Usage

contourpl(input)

Arguments

Value

The contour plot

Author(s)

Cristina Tortora Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

Examples

##loading bankruptcy data
data(bankruptcy)

##model estimation
res=MCGHD(data=bankruptcy[,2:3],G=2,method="kmedoids",max.iter=30)
#result
contourpl(res)

Density of a coalesced generalized hyperbolic distribution (MSGHD).

Description

Compute the density of a p dimensional coalesced generalized hyperbolic distribution.

Usage

dCGHD(data,p,mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),lambda=1,omega=1,
  omegav=rep(1,p),lambdav=rep(1,p),wg=0.5,gam=NULL,phi=NULL)

Arguments

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n dimensional vector with the density from a coalesced generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification (to appear).

Examples

x = seq(-3,3,length.out=30)
y = seq(-3,3,length.out=30)
xyS1 = matrix(0,nrow=length(x),ncol=length(y))
for(i in 1:length(x)){
  for(j in 1:length(y)){
      xy <- matrix(cbind(x[i],y[j]),1,2)	
      xyS1[i,j] =  dCGHD(xy,2) 
      
    }
  }
contour(x=x,y=y,z=xyS1, levels=c(.005,.01,.025,.05, .1,.25), main="CGHD",ylim=c(-3,3), xlim=c(-3,3))

Density of a generalized hyperbolic distribution (GHD).

Description

Compute the density of a p dimensional generalized hyperbolic distribution.

Usage

dGHD(data,p, mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),omega=1,lambda=0.5, log=FALSE)

Arguments

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n dimensional vector with the density from a generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

R.P. Browne, and P.D. McNicholas (2015). A Mixture of Generalized Hyperbolic Distributions. Canadian Journal of Statistics, 43.2 176-198

Examples

x = seq(-3,3,length.out=50)
y = seq(-3,3,length.out=50)
xyS1 = matrix(0,nrow=length(x),ncol=length(y))
for(i in 1:length(x)){
  for(j in 1:length(y)){
      xy <- matrix(cbind(x[i],y[j]),1,2)	
      xyS1[i,j] =  dGHD(xy,2) 
      
    }
  }
contour(x=x,y=y,z=xyS1, levels=c(.005,.01,.025,.05, .1,.25), main="MGHD",ylim=c(-3,3), xlim=c(-3,3))

Density of a mulitple-scaled generalized hyperbolic distribution (MSGHD).

Description

Compute the density of a p dimensional mulitple-scaled generalized hyperbolic distribution.

Usage

dMSGHD(data,p,mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),omegav=rep(1,p),
 lambdav=rep(0.5,p),gam=NULL,phi=NULL,log=FALSE)

Arguments

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n dimensional vector with the density from a multiple-scaled generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification (to appear).

Examples

x = seq(-3,3,length.out=50)
y = seq(-3,3,length.out=50)
xyS1 = matrix(0,nrow=length(x),ncol=length(y))
for(i in 1:length(x)){
  for(j in 1:length(y)){
      xy <- matrix(cbind(x[i],y[j]),1,2)	
      xyS1[i,j] =  dMSGHD(xy,2) 
      
    }
  }
contour(x=x,y=y,z=xyS1, levels=seq(.005,.25,by=.005), main="MSGHD")

Plot objects of class MixGHD.

Description

Plots the loglikelyhood function and for p<10 shows the splom of the data.

Usage

	## S4 method for signature 'MixGHD'
plot(x,y)

Arguments

;

Details

Plot the loglikhelyhood vale for each iteration of the EM algorithm. If p=2 it shows a contour plot. If 2<p<10 shows a splom of the data colored according to the cluster membership.

Methods

signature(x = "MixGHD", y = "missing")

S4 method for plotting objects of MixGHD-class.

Author(s)

Cristina Tortora. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

See Also

MixGHD-class,MGHD,MCGHD,MSGHD,cMSGHD,MGHFA

Examples

##loading banknote data
data(bankruptcy)


##model estimation
model=MCGHD(bankruptcy[,2:3],G=2,max.iter=30)

#result

plot(model)

Membership prediction for objects of class MixGHD

Description

Cluster membership

Usage

	## S4 method for signature 'MixGHD'
predict(object)

Arguments

Value

The cluster membership

Author(s)

Cristina Tortora Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

Examples

##loading bankruptcy data
data(bankruptcy)

##model estimation
res=MCGHD(data=bankruptcy[,2:3],G=2,method="kmedoids",max.iter=30)
#rcoefficients of the model
predict(res)

Pseudo random number generation from a coalesced generalized hyperbolic distribution (MSGHD).

Description

Generate n pseudo random numbers from a p dimensional coalesced generalized hyperbolic distribution.

Usage

rCGHD(n,p,mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),omega=1,lambda=0.5
,omegav=rep(1,p),lambdav=rep(0.5,p),wg=0.5)

Arguments

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n times p matrix of numbers psudo randomly generated from a coalesced generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification (to appear).

Examples

data=rCGHD(300,2,alpha=c(2,-2),omegav=c(2,2),omega=3)

plot(data)

Pseudo random number generation from a generalized hyperbolic distribution (GHD).

Description

Generate n pseudo random numbers from a p dimensional generalized hyperbolic distribution.

Usage

rGHD(n,p, mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),omega=1,lambda=0.5)

Arguments

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n times p matrix of numbers psudo randomly generated from a generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

R.P. Browne, and P.D. McNicholas (2015). A Mixture of Generalized Hyperbolic Distributions. Canadian Journal of Statistics, 43.2 176-198

Examples

data=rGHD(300,2,alpha=c(2,-2))

plot(data)

Pseudo random number generation from a mulitple-scaled generalized hyperbolic distribution (MSGHD).

Description

Generate n pseudo random numbers from a p dimensional mulitple-scaled generalized hyperbolic distribution.

Usage

rMSGHD(n,p, mu=rep(0,p),alpha=rep(0,p),sigma=diag(p),omegav=rep(1,p),lambdav=rep(0.5,p))

Arguments

Details

The default values are: 0 for the mean and the skweness parameter alpha, diag(p) for sigma, 1 for omega, and 0.5 for lambda.

Value

A n times p matrix of numbers psudo randomly generated from a generilzed hyperbolic distribution

Author(s)

Cristina Tortora, Aisha ElSherbiny, Ryan P. Browne, Brian C. Franczak, and Paul D. McNicholas. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

References

C. Tortora, B.C. Franczak, R.P. Browne, and P.D. McNicholas (2019). A Mixture of Coalesced Generalized Hyperbolic Distributions. Journal of Classification (to appear).

Examples

data=rMSGHD(300,2,alpha=c(2,-2),omegav=c(2,2))

plot(data)

Sonar data

Description

The data report the patterns obtained by bouncing sonar signals at various angles and under various conditions. There are 208 patterns in all, 111 obtained by bouncing sonar signals off a metal cylinder and 97 obtained by bouncing signals off rocks. Each pattern is a set of 60 numbers (variables) taking values between 0 and 1.

Usage

data(sonar)

Format

A data frame with 208 observations and 61 columns. The first 60 columns contain the variables. The 61st column gives the material: 1 rock, 2 metal.

Source

UCI machine learning repository

References

R.P. Gorman and T. J. Sejnowski (1988) Analysis of hidden units in a layered network trained to classify sonar targets. Neural Networks 1: 75-89

Plot objects of class MixGHD.

Description

Methods for function summary aimed at summarizing the S4 classes included in the MixGHD-package

Arguments

Methods

signature(object = "MixGHD")

S4 method for summaryzing objects of MixGHD-class.

Author(s)

Cristina Tortora. Maintainer: Cristina Tortora <cristina.tortora@sjsu.edu>

See Also

MixGHD MixGHD-class,MGHD,MCGHD,MSGHD,cMSGHD,MGHFA

Examples

##loading banknote data
data(bankruptcy)


##model estimation
model=MSGHD(bankruptcy[,2:3],G=2,max.iter=30)

#result

summary(model)