R: Cauchy-polynomial quantile mixture

cauchypoly {Lmoments} | R Documentation

## 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 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

`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');

[Package Lmoments version 1.2-3 Index]