This is an attempt to create a distribution function if the only existing information is the quantiles or expectiles of the distribution.
1 2 3 4 5 
quantiles 
a list with components 
expectiles 
a list with components 
lambda 
smoothing parameter for the logpdf 
kappa 
smoothing parameter for log concavity 
delta 
smoothing parameter for ridge penalty 
order 
the order of the penalty for logpdf 
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 
... 
additional arguments 
Returns a list with components
pdf 
the hights of the fitted pdf, the sum of it multiplied by the Dx should add up to 1 i.e. 
cdf 
the fitted cdf 
x 
the values of x where the discretise distribution is defined 
pFun 
the cdf of the fitted nonparametric distribution 
qFun 
the inverse cdf function of the fitted nonparametric distribution 
rFun 
a function to generate a random sample from the fitted nonparametric distribution 
Mikis Stasinopoulos, Paul Eilers, Bob Rigby and Vlasios Voudouris
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 507554.
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.
1 2 3 4 5 6 7 8 9  # 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)#

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