data2cauchypoly {Lmoments}

Estimation of the Cauchy-polynomial quantile mixture

Description

Estimates the parameters of the Cauchy-polynomial quantile mixture from data or from trimmed L-moments

Usage

data2cauchypoly4(data)
t1lmom2cauchypoly4(t1lmom)

Arguments

data

vector

t1lmom

vector of trimmed L-moments

Value

vector containing the four parameters of the Cauchy-polynomial quantile mixture

Author(s)

Juha Karvanen [e-mail]

References

Karvanen, J. 2006. Estimation of quantile mixtures via L-moments and trimmed L-moments, Computational Statistics & Data Analysis 51, (2), 947–959. http://www.bsp.brain.riken.jp/publications/2006/karvanen_quantile_mixtures.pdf.

See Also

t1lmoments for trimmed L-moments, dcauchypoly for the Cauchy-polynomial quantile mixture and data2normpoly4 for the estimation of the normal-polynomial quantile mixture.

Examples

#Generates 500 random variables from the Cauchy-polynomial quantile mixture, 
#calculates the trimmed L-moments,
#estimates parameters via trimmed L-moments and 
#plots the true pdf and the estimated pdf together with the histogram of the data.
true_params<-t1lmom2cauchypoly4(c(0,1,0.075,0.343));
x<-rcauchypoly(500,true_params);
t1lmom<-t1lmoments(x);
estim_params<-t1lmom2cauchypoly4(t1lmom);
plotpoints<-seq(-10,10,by=0.01);
histpoints<-c(seq(min(x)-1,-20,length.out=50),seq(-10,10,by=0.5),seq(20,max(x)+1,length.out=50));
hist(x,breaks=histpoints,freq=FALSE,xlim=c(-10,10));
lines(plotpoints,dcauchypoly(plotpoints,estim_params),col='red');
lines(plotpoints,dcauchypoly(plotpoints,true_params),col='blue');