flexDist: Non-parametric pdf from limited information data

In gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

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

pdf	the 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])
cdf	the fitted cdf
x	the values of x where the discretise distribution is defined
pFun	the cdf of the fitted non-parametric distribution
qFun	the inverse cdf function of the fitted non-parametric distribution
rFun	a function to generate a random sample from the fitted non-parametric distribution

Author(s)

Mikis Stasinopoulos, Paul Eilers, Bob Rigby and Vlasios Voudouris

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/9780429298547")}. An older version can be found in https://www.gamlss.com/.

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v023.i07")}.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/b21973")}

(see also https://www.gamlss.com/).

See Also

histSmo

Examples

# 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)# 

gamlss.dist documentation built on Aug. 24, 2023, 1:06 a.m.