R: Normal-polynomial quantile mixture

normpoly {Lmoments} | R Documentation

## Normal-polynomial quantile mixture

### Description

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

### Usage

    dnormpoly(x,param)
    pnormpoly(x,param)
    qnormpoly(cp,param)
    rnormpoly(n,param)
    normpoly_pdf(x,param)
    normpoly_cdf(x,param)
    normpoly_inv(cp,param)
    normpoly_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 normal distribution. (Functions normpoly\_pdf, normpoly\_cdf, normpoly\_inv and normpoly\_rnd are aliases for compatibility with older versions of this package.)

### Value

'dnormpoly' gives the density, 'pnormpoly' gives the cumulative distribution function, 'qnormpoly' gives the quantile function, and 'rnormpoly' 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

`data2normpoly4` for the parameter estimation and `dcauchypoly` for the Cauchy-polynomial quantile mixture.

### Examples

    #Generates a sample 500 observations from the normal-polynomial quantile mixture,
    #calculates L-moments and their covariance matrix,
    #estimates parameters via L-moments and
    #plots the true pdf and the estimated pdf together with the histogram of the data.
    true_params<-lmom2normpoly4(c(0,1,0.2,0.05));
    x<-rnormpoly(500,true_params);
    lmoments<-Lmoments(x);
    lmomcov<-Lmomcov(x);
    estim_params<-lmom2normpoly4(lmoments);
    hist(x,30,freq=FALSE)
    plotpoints<-seq(min(x)-1,max(x)+1,by=0.01);
    lines(plotpoints,dnormpoly(plotpoints,estim_params),col='red');
    lines(plotpoints,dnormpoly(plotpoints,true_params),col='blue');

[Package Lmoments version 1.2-3 Index]