cauchypoly {Lmoments}

Cauchy-polynomial quantile mixture

Description

Density, distribution function, quantile function and random generation for the Cauchy-polynomial quantile mixture.

Usage

dcauchypoly(x,param)
pcauchypoly(x,param)
qcauchypoly(cp,param)
rcauchypoly(n,param)
cauchypoly_pdf(x,param)
cauchypoly_cdf(x,param)
cauchypoly_inv(cp,param)
cauchypoly_rnd(n,param)

Arguments

x

vector of quantiles

cp

vector of probabilities

n

number of observations

param

vector of parameters

Details

The length the parameter vector specifies the order of the polynomial in the quantile mixture. If k<-length(param) then param[1:(k-1)] contains the mixture coefficients of polynomials starting from the constant and param[k] is the mixture coefficient for Cauchy distribution. (Functions cauchypoly\_pdf, cauchypoly\_cdf, cauchypoly\_inv and cauchypoly\_rnd are aliases for compatibility with older versions of this package.)

Value

'dcauchypoly' gives the density, 'pcauchypoly' gives the cumulative distribution function, 'qcauchypoly' gives the quantile function, and 'rcauchypoly' generates random deviates.

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

data2cauchypoly4 for the parameter estimation and dnormpoly for 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');