normpoly {Lmoments} | R Documentation |
Density, distribution function, quantile function and random generation for the normal-polynomial quantile mixture.
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)
x |
vector of quantiles |
cp |
vector of probabilities |
n |
number of observations |
param |
vector of parameters |
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.)
'dnormpoly' gives the density, 'pnormpoly' gives the cumulative distribution function, 'qnormpoly' gives the quantile function, and 'rnormpoly' generates random deviates.
Juha Karvanen juha.karvanen@ktl.fi
Karvanen, J. 2005. Estimation of quantile mixtures via L-moments and trimmed L-moments, Computational Statistics & Data Analysis, in press, http://www.bsp.brain.riken.jp/publications/2005/karvanen_quantile_mixtures.pdf.
data2normpoly4
for the parameter estimation and
dcauchypoly
for the Cauchy-polynomial quantile mixture.
#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');