flexDist: Non-parametric pdf from limited information data

Description

This is an attempt to create a distribution function if the only existing information is the quantiles or expectiles of the distribution.

Usage

flexDist(quantiles = list(values=c(-1.96,0,1.96), prob=c(0.05, .50, 0.95)), 
         expectiles = list(), lambda = 10, 
         kappa = 10, delta = 1e-07, order = 3, n.iter = 200, 
         plot = TRUE, no.inter = 100, lower = NULL, 
         upper = NULL, perc.quant = 0.3, ...)

Arguments

quantiles

a list with components values and prob

expectiles

a list with components values and prob

lambda

smoothing parameter for the log-pdf

kappa

smoothing parameter for log concavity

delta

smoothing parameter for ridge penalty

order

the order of the penalty for log-pdf

n.iter

maximum number of iterations

plot

whether to plot the result

no.inter

How many discrete probabilities to evaluate

lower

the lower value of the x

upper

the upper value of the x

perc.quant

how far from the quantile should go out to define the limit of x if not set by lower or upper

...

additional arguments

Value

Returns a list with components
pdfthe hights of the fitted pdf, the sum of it multiplied by the Dx should add up to 1 i.e. sum(object$pdf*diff(object$x)[1])
cdfthe fitted cdf
xthe values of x where the discretise distribution is defined
pFunthe cdf of the fitted non-parametric distribution
qFunthe inverse cdf function of the fitted non-parametric distribution
rFuna function to generate a random sample from the fitted non-parametric distribution

References

Eilers, P. H. C., Voudouris, V., Rigby R. A., Stasinopoulos D. M. (2012) Estimation of nonparametric density from sparse summary information, under review. Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Examples

Run this code

# Normal
r1<-flexDist(quantiles=list(values=qNO(c(0.05, 0.25, 0.5,0.75, 0.95), mu=0, 
             sigma=1), prob=c( 0.05, 0.25, 0.5,0.75,0.95 )), 
             no.inter=200, lambda=10,  kappa=10, perc.quant=0.3)
# GAMMA
r1<-flexDist(quantiles=list(values=qGA(c(0.05,0.25, 0.5,0.75,0.95), mu=1, 
       sigma=.8), prob=c(0.05,0.25, 0.5,0.75,0.95)), 
       expectiles=list(values=1, prob=0.5),  lambda=10, 
       kappa=10, lower=0, upper=5)#