R: Estimation of the Cauchy-polynomial quantile mixture

data2cauchypoly {Lmoments} | R Documentation

## 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 juha.karvanen@iki.fi

### 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');

[Package Lmoments version 1.2-3 Index]