The mlCopulaSelection Package - uni-bayreuth.deftp.uni-bayreuth.de/math/statlib/R/CRAN/doc/packages/mlCopula... · The mlCopulaSelection Package October 15, 2006 ... v Second coordenate

The mlCopulaSelection PackageOctober 15, 2006

Type Package

Title Copula selection and fitting using maximum likelihood

Version 1.3

Date 2006-08-12

Author Jesus Garcia and Veronica Gonzalez-Lopez

Maintainer Jesus Garcia <[email protected]>

Description Use numerical maximum likelihood to choose and fit a bivariate copula model (from alibrary of 40 models) to the data.

License GPL version 2.

R topics documented:clibmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2dcbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3dcbb10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4dcbb2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5dcbb3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6dcbb4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7dcbb5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8dcbb6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9dcbb7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10dcbb8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11dcbb9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12llbb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14llbb10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18llbb5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19llbb6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20llbb7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21llbb8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22llbb9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23mlCopulaSelection-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1

2 clibmodel

mlcbb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25mlcbbsel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Index 30

clibmodel Auxiliary function used by the function mlcbbsel

Description

Auxiliary function used by the function mlcbbsel

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

## The function is currently defined asfunction(param,x,y, model = c("CBB1", "CBB2", "CBB3", "CBB4", "CBB5", "CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")) {model <- match.arg(model)switch(model,

CBB1 = llbb1(param,x,y),CBB2 = llbb2(param,x,y),CBB3 = llbb3(param,x,y),CBB4 = llbb4(param,x,y),CBB5 = llbb5(param,x,y),CBB6 = llbb6(param,x,y),CBB7 = llbb7(param,x,y),CBB8 = llbb8(param,x,y),CBB9 = llbb9(param,x,y),CBB10 = llbb10(param,x,y),CMM1 = llbb1(param,1-x,1-y),CMM2 = llbb2(param,1-x,1-y),CMM3 = llbb3(param,1-x,1-y),CMM4 = llbb4(param,1-x,1-y),CMM5 = llbb5(param,1-x,1-y),CMM6 = llbb6(param,1-x,1-y),CMM7 = llbb7(param,1-x,1-y),CMM8 = llbb8(param,1-x,1-y),CMM9 = llbb9(param,1-x,1-y),CMM10 = llbb10(param,1-x,1-y),CBM1 = llbb1(param,x,1-y),CBM2 = llbb2(param,x,1-y),CBM3 = llbb3(param,x,1-y),CBM4 = llbb4(param,x,1-y),CBM5 = llbb5(param,x,1-y),CBM6 = llbb6(param,x,1-y),CBM7 = llbb7(param,x,1-y),

dcbb1 3

CBM8 = llbb8(param,x,1-y),CBM9 = llbb9(param,x,1-y),CBM10 = llbb10(param,x,1-y),CMB1 = llbb1(param,1-x,y),CMB2 = llbb2(param,1-x,y),CMB3 = llbb3(param,1-x,y),CMB4 = llbb4(param,1-x,y),CMB5 = llbb5(param,1-x,y),CMB6 = llbb6(param,1-x,y),CMB7 = llbb7(param,1-x,y),CMB8 = llbb8(param,1-x,y),CMB9 = llbb9(param,1-x,y),CMB10 = llbb10(param,1-x,y))

}

dcbb1 BB1 copula density function

Description

Calculate the value of the BB1 density.

Usage

dcbb1(theta, delta, u, v)

Arguments

theta Parameter theta of the BB1. (0<theta)

delta Parameter delta of the BB1. (1<delta)

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB1 for the parameters theta and delta on ( u , v )

Author(s)


References


4 dcbb10

Examples

res<-dcbb1(0.5,1.5,0.90,0.85)

## The function is currently defined asfunction(theta,delta,u,v){S<-u^(-theta)-1;T<-v^(-theta)-1;-10**(4)W<-S^(delta)+T^(delta);DuS<-(-theta)*u^(-theta-1);DuW<-delta*S^(delta-1)*DuS;DvT<-(-theta)*v^(-theta-1);DvW<-delta*T^(delta-1)*DvT;densi<-(-1/(theta*delta))*(-1/theta-1)*(1+W^(1/delta))^(-1/theta-2)*(1/delta)*W^(1/delta-1)*DvW*W^(1/delta-1)*DuW-(1/(theta*delta))*(1+W^(1/delta))^(-1/theta-1)*(1/delta-1)*W^(1/delta-2)*DvW*DuW}


Description


Usage


Arguments

theta Parameter theta of the BB10, (0<theta<1).

delta Parameter delta of the BB10, (0<delta).



Value


Author(s)


References


dcbb2 5

Examples

res<-dcbb10(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){S<-1-u^(1/delta);T<-1-v^(1/delta);W<-theta*S*T;C<-u*v*(1-W)^(-delta);DuS<-(-1/delta)*u^(1/delta-1);DuW<-theta*T*DuS;DvT<-(-1/delta)*v^(1/delta-1);DvW<-theta*S*DvT;DvuW<-theta*DuS*DvT;densi<-(1-W)^(-delta)+v*(-delta)*(1-W)^(-delta-1)*(-1)*DvW+u*delta*(1-W)^(-delta-1)*DuW+u*v*delta*(-delta-1)*(1-W)^(-delta-2)*(-1)*DvW*DuW+u*v*delta*(1-W)^(-delta-1)*DvuW}


Description


Usage


Arguments

theta Parameter theta of the BB2, (0<theta).




Value


Author(s)


References


6 dcbb3

Examples

res<-dcbb2(0.5,0.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){k<-exp(theta*(u^(-delta)-1));t<-exp(theta*(v^(-delta)-1));S<-k+t-1;h<-(1/theta)*log(S);duk<--k*(theta*delta)*u^(-delta-1);dvt<--t*(theta*delta)*v^(-delta-1);duS<-duk;dvS<-dvt;duh<-(1/theta)*duS/S;dvh<-(1/theta)*dvS/S;dvuh<-(-1/theta)*duS*dvS/S^2;densi<-(1/delta)*(1+1/delta)*(1+h)^(-2-1/delta)*dvh*duh-(1/delta)*(1+h)^(-1-1/delta)*dvuh

}


Description


Usage


Arguments





Value


Author(s)


References


dcbb4 7

Examples

res<-dcbb3(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){W<-exp(theta*(-log(u))^(delta));P<-exp(theta*(-log(v))^(delta));S<-W+P-1;h<-(1/theta)*log(S);F<-exp(-h^(1/delta));duS<-exp((-log(u))^(delta)*theta)*(-theta*delta/u)*(-log(u))^(delta-1);dvS<-exp((-log(v))^(delta)*theta)*(-theta*delta/v)*(-log(v))^(delta-1);dvuh<-(-1/theta)/S^2*duS*dvS;duh<-(1/theta)*duS/S;dvh<-(1/theta)*dvS/S;densi<-F*(1/delta^2)*(h^(1/delta-1))^2*dvh*duh+F*(-1/delta)*(1/delta-1)*(h)^(1/delta-2)*(dvh)*(duh)+F*(-1/delta)*(h)^(1/delta-1)*dvuh}


Description


Usage


Arguments





Value


Author(s)


References


8 dcbb5

Examples

res<-dcbb4(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){VV<-(u^(-theta)-1)^(-delta);

WW<-(v^(-theta)-1)^(-delta);h<-VV+WW;S<-u^(-theta)+v^(-theta)-1;duh<-delta*theta*u^(-theta-1)*(u^(-theta)-1)^(-delta-1);dvh<-delta*theta*v^(-theta-1)*(v^(-theta)-1)^(-delta-1);duS<-(-theta)*u^(-theta-1);dvS<-(-theta)*v^(-theta-1);densi<-(1/theta)*(1/theta+1)*(S-h^(-1/delta))^(-1/theta-2)*(dvS+1/delta*h^(-1/delta-1)*dvh)*(duS+1/delta*h^(-1/delta-1)*duh)+(-1/theta)*(S-h^(-1/delta))^(-1/theta-1)*((-1/delta)*(1/delta+1)*(h)^(-1/delta-2)*dvh*duh)}


Description


Usage


Arguments





Value


Author(s)


References


dcbb6 9

Examples

res<-dcbb5(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){t<-(-log(u))^(-theta*delta)+(-log(v))^(-theta*delta);

dut<-(theta*delta/u)*(-log(u))^(-theta*delta-1);dvt<-(theta*delta/v)*(-log(v))^(-theta*delta-1);S<-(-log(u))^(theta)+(-log(v))^(theta);duS<-(-theta/u)*(-log(u))^(theta-1);dvS<-(-theta/v)*(-log(v))^(theta-1);h<-S-t^(-1/delta);duh<-duS+(1/delta)*(t)^(-1/delta-1)*(dut);dvh<-dvS+(1/delta)*(t)^(-1/delta-1)*(dvt);dvuh<--1/delta*(1/delta+1)*t^(-1/delta-2)*dut*dvt;densi<-exp(-h^(1/theta))*(1/theta)^2*(h^(1/theta-1))^2*dvh*duh+exp(-h^(1/theta))*(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh+exp(-h^(1/theta))*(-1/theta)*h^(1/theta-1)*dvuh}


Description


Usage

dcbb6(t, d, u, v)

Arguments

t Parameter t of the BB6, (1<t).

d Parameter d of the BB6, (1<d).



Value

value of de density BB6 for the parameters t and d on ( u , v )

Author(s)


References


10 dcbb7

Examples

res<-dcbb6(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(t,d,u,v){

t19 = (d*t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d-1.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-1.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))-(t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**2*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(2./d-2.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(1./t-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-2.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))+(d*t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**2*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d-2.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(1./d-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-1.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))}


Description


Usage


Arguments





Value


Author(s)


References


Examples

res<-dcbb7(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){WU<-(1-(1-u)^(theta))^(-delta);

WV<-(1-(1-v)^(theta))^(-delta);duWU<-(-delta*theta)*(1-(1-u)^(theta))^(-delta-1)*(1-u)^(theta-1);

dcbb8 11

dvWV<-(-delta*theta)*(1-(1-v)^(theta))^(-delta-1)*(1-v)^(theta-1);K<-WU+WV;duK<-duWU;dvK<-dvWV;S<-K-1;duS<-duK;dvS<-dvK;h<-1-S^(-1/delta);duh<-(1/delta)*S^(-1/delta-1)*duS;dvh<-(1/delta)*S^(-1/delta-1)*dvS;dvuh<-(1/delta)*(-1/delta-1)*(S)^(-1/delta-2)*(dvS)*(duS);densi<-(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh-(1/theta)*h^(1/theta-1)*dvuh}


Description


Usage


Arguments


delta Parameter delta of the BB8, (0<delta<1).



Value


Author(s)


References


12 dcbb9

Examples

res<-dcbb8(1.5,0.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){S<-1-(1-delta*u)^(theta);T<-1-(1-delta*v)^(theta);K<-(1-(1-delta)^(theta))^(-1);W<-1-K*S*T;DuS<-theta*delta*(1-delta*u)^(theta-1);DuW<--K*T*DuS;DvT<-theta*delta*(1-delta*v)^(theta-1);DvW<--K*S*DvT;DvuW<--K*DuS*DvT;densi<--delta^(-1)*(1/theta)*(1/theta-1)*W^(1/theta-2)*DvW*DuW-delta^(-1)*(1/theta)*W^(1/theta-1)*DvuW}


Description


Usage


Arguments





Value


Author(s)


References


llbb 13

Examples

res<-dcbb9(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){S<-delta-log(u);T<-delta-log(v);W<-S^(theta)+T^(theta)-delta^(theta);C<-exp(-W^(1/theta)+delta);DuS<--1/u;DuW<-theta*S^(theta-1)*DuS;DvT<--1/v;DvW<-theta*T^(theta-1)*DvT;densi<-C*(1/theta^2)*(W^(1/theta-1))^2*DvW*DuW+C*(-1/theta)*(1/theta-1)*W^(1/theta-2)*DvW*DuW}

llbb Auxiliary function used by the function mlcbbsel

Description


Author(s)


References


Examples

## The function is currently defined asfunction(param,u,v, model = c("CBB1", "CBB2", "CBB3", "CBB4", "CBB5", "CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")){n<-sum(u>=-1)ss<-c(1:n)*0s<-0.for(i in 1:n) { ss[i]<-log(cbbmodel(param[1],param[2],u[i],v[i],model)) }res<-ss}

14 llbb1

llbb1 BB1’s log-likelihood function

Description

Calculate the log-likelihood for the BB1 density.

Usage

llbb1(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta and 1<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB1’s log-likelihood function for the sample

Author(s)


References


Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb1(c(0.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log( dcbb1(param[1],param[2],u[i],v[i]) );if(is.nan(s)) {break};}if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

llbb10 15


Description


Usage

llbb10(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta<1 and 0<delta)



Details


Value


Author(s)


References


Examples


## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb10(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

16 llbb1


Description


Usage

llbb2(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



llbb1 17


Description


Usage

llbb3(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



18 llbb1


Description


Usage

llbb4(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



llbb5 19


Description


Usage

llbb5(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



20 llbb6


Description


Usage

llbb6(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



llbb7 21


Description


Usage

llbb7(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



22 llbb8


Description


Usage

llbb8(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (1<theta and 0<delta<1)



Details


Value


Author(s)


References


Examples



llbb9 23


Description


Usage

llbb9(param, u, v)

Arguments




Details


Value


Author(s)


References


Examples



24 mlCopulaSelection-package

mlCopulaSelection-packageCopula selection and fitting using maximum likelihood

Description

Use numerical maximum likelihood to choose and fit a bivariate copula model (from a library of 40models) to the data. The copula models in the library correspond to BB1, BB2,...,BB10 from Joe,H., (1997) and its 90, 180 and 270 degree rotations.

Details

Package: mlCopulaSelectionType: PackageVersion: 1.3Date: 2006-08-12License: GPL version 2.

Author(s)


Maintainer: Jesus Garcia <[email protected]>

References


Examples

# The Data (the margins are uniform)U <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)V <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# find the maximun likelihood estimatesres<-mlcbbsel(U,V)#the best fitting copula model:res$copmax#the parameters for the best fitting copula model:res$parmax#the log-likelihood of the best fitting copula model with those parameters:res$llmax

mlcbb 25

mlcbb Auxiliary function used by the function mlcbbsel

Description


Author(s)


References


Examples

## The function is currently defined asfunction(u,v,thetamin,deltamin,thetamax,deltamax, copulamodel=c("CBB1","CBB2" , "CBB3","CBB4","CBB5","CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")){PMAX<-0

DMAX<-20TMAX<-20if(missing(deltamax)){deltamax<- DMAX}if(missing(thetamax)){thetamax<- TMAX}

if(missing(deltamin) && copulamodel=="CBB1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBB2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBB4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBB7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CBB8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CBB8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CBB9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB10"){deltamin<-0.005};

if(missing(deltamin) && copulamodel=="CMM1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMM2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMM4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMM7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CMM8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CMM8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CMM9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM10"){deltamin<-0.005};

26 mlcbb

if(missing(deltamin) && copulamodel=="CBM1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBM2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBM4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBM7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CBM8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CBM8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CBM9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM10"){deltamin<-0.005};

if(missing(deltamin) && copulamodel=="CMB1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMB2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMB4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMB7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CMB8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CMB8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CMB9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB10"){deltamin<-0.005};

if(missing(thetamin) && copulamodel=="CBB1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CBB10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CBB10"){thetamax<-0.995}

if(missing(thetamin) && copulamodel=="CMM1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CMM10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CMM10"){thetamax<-0.995}

mlcbbsel 27

if(missing(thetamin) && copulamodel=="CBM1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CBM10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CBM10"){thetamax<-0.995}

if(missing(thetamin) && copulamodel=="CMB1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CMB10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CMB10"){thetamax<-0.995}

n<-sum(u>=-1)m<-5inct<-(thetamax-thetamin)/(m+1)incd<-(deltamax-deltamin)/(m+1)PMAX <- -10**(250)for (tet in 1:m){ for (del in 1:m){teta <- thetamin + tet*inctdelta <- deltamin + del*incd

pvalor<-clibmodel(c(teta,delta),u,v,model=copulamodel)

if (pvalor>PMAX) { PMAX <- pvalor; tlmax<- teta ; dlmax <- delta }} }

result<-optim(c(tlmax,dlmax), method = "L-BFGS-B" , clibmodel,lower = c(thetamin,deltamin), upper = c(thetamax,deltamax) , control=list(fnscale=-1), x=u , y=v , model = copulamodel )

}

mlcbbsel Function for maximum likelihood copula selection and fitting

28 mlcbbsel

Description

Use numerical maximum likelihood to choose and fit a bivariate copula model (from a library of 40models) to the data.

Usage

mlcbbsel(U, V)

Arguments

U vector with the first coordenate of the bivariate data

V vector with the second coordenate of the bivariate data (same size asU)

Details

(U,V) margins must have Uniform(0,1) marginal distribution

Value

It return a LIST with,

copmax the best fitting copula model. The copula models in the library correspond toBB1, BB2,...,BB10 from Joe, H., (1997) and its 90, 180 and 270 degree rota-tions.

parmax the maximum likelihood estimates of the parameters for the best fitting copula

llmax the log-likelihood on the estimated parameters for the best copula

todo contain a matrix with the maximum likelihood ressults for all the copula models.The first column is the copulamodel number (from 1 to 40), the second columnis the maximum log-likelihood for that particular model and the third and fourthcolumn contain the parameters values for which that maximum log-likelihoodwas attained.

Author(s)

Jesus Garcia. IMECC-UNICAMP and Veronica Gonzalez-Lopez. IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hal l.

Examples

# The Data (the margins are uniform)U <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)V <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# find the maximun likelihood estimatesres<-mlcbbsel(U,V)#the best fitting copula model:res$copmax#the parameters for the best fitting copula model:res$parmax#the log-likelihood of the best fitting copula model with those parameters:

mlcbbsel 29

res$llmax

## The function is currently defined asfunction(U,V){

model=c("CBB1","CBB2" , "CBB3","CBB4","CBB5","CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")

respmodel=c("CBB1","CBB2" , "CBB3","CBB4","CBB5","CBB6", "CBB7","CBB8", "CBB9", "CBB10","180 degree rotation of CBB1","180 degree rotation of CBB2" , "180 degree rotation of CBB3","180 degree rotation of CBB4","180 degree rotation of CBB5","180 degree rotation of CBB6", "180 degree rotation of CBB7","180 degree rotation of CBB8", "180 degree rotation of CBB9", "180 degree rotation of CBB10","90 degree rotation of CBB1","90 degree rotation of CBB2" , "90 degree rotation of CBB3","90 degree rotation of CBB4","90 degree rotation of CBB5","90 degree rotation of CBB6", "90 degree rotation of CBB7","90 degree rotation of CBB8", "90 degree rotation of CBB9", "90 degree rotation of CBB10","270 degree rotation of CBB1","270 degree rotation of CBB2" , "270 degree rotation of CBB3","270 degree rotation of CBB4","270 degree rotation of CBB5","270 degree rotation of CBB6", "270 degree rotation of CBB7","270 degree rotation of CBB8", "270 degree rotation of CBB9", "270 degree rotation of CBB10")

ncop<-1

TODOCOP <-c(1:40)TODOPV <-c(1:2)*0TODOTET <-c(1:2)*0TODODEL <-c(1:2)*0PVMAX<- -10**(100)pmax<-10

n<-sum(U != -10**200)

for(nmodel in 1:40){RES <- mlcbb(U,V,copulamodel=model[nmodel])PV <- RES$valuePAR<- RES$parif (PV>PVMAX) {PVMAX<-PV;PARMAX<-PAR;COPMAX<-nmodel;LLMAX<-PV}TODOPV[nmodel]<- PVTODOTET[nmodel] <-PAR[1]TODODEL[nmodel] <-PAR[2]}

ORDEN<-order(TODOPV,TODOCOP,decreasing= TRUE)

TODO<-matrix(c(1:40*4)*0,40,4)

TODO[,1]<-respmodel[TODOCOP[ORDEN]]TODO[,2]<-TODOPV[ORDEN]TODO[,3]<-TODOTET[ORDEN]TODO[,4]<-TODODEL[ORDEN]

result <- list(todo=TODO,copmax=respmodel[COPMAX],parmax=PARMAX,llmax=LLMAX)}

Index

∗Topic documentationmlCopulaSelection-package, 23

∗Topic internalclibmodel, 1llbb, 12mlcbb, 24

∗Topic miscdcbb1, 2dcbb10, 3dcbb2, 4dcbb3, 5dcbb4, 6dcbb5, 7dcbb6, 8dcbb7, 9dcbb8, 10dcbb9, 11llbb1, 13, 15–17llbb10, 14llbb5, 18llbb6, 19llbb7, 20llbb8, 21llbb9, 22mlcbbsel, 26

clibmodel, 1

dcbb1, 2dcbb10, 3dcbb2, 4dcbb3, 5dcbb4, 6dcbb5, 7dcbb6, 8dcbb7, 9dcbb8, 10dcbb9, 11

llbb, 12llbb1, 13, 15–17llbb10, 14llbb2 (llbb1), 15llbb3 (llbb1), 16

llbb4 (llbb1), 17llbb5, 18llbb6, 19llbb7, 20llbb8, 21llbb9, 22

mlcbb, 24mlcbbsel, 26mlCopulaSelection

(mlCopulaSelection-package),23

mlCopulaSelection-package, 23

30

Documents

The mlCopulaSelection Package - uni-bayreuth.deftp.uni-bayreuth.de/math/statlib/R/CRAN/doc/packages/mlCopula... · The mlCopulaSelection Package October 15, 2006 ... v Second coordenate