Lmoments (version 1.3-1)

normpoly: 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

Value

'dnormpoly' gives the density, 'pnormpoly' gives the cumulative distribution function, 'qnormpoly' gives the quantile function, and 'rnormpoly' generates random deviates.

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.)

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

# NOT RUN {
#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');
# }