intF {logcondens} | R Documentation |
Computes the Integral of the estimated CDF at Arbitrary Real Numbers in s
Description
Based on an object of class dlc
as output by the function logConDens
,
this function gives values of
at all numbers in . Note that
(so all elements in
) must lie in
. The exact formula for
is
where min
and
for ,
for any vector
and the function
introduced in
Jfunctions
.
Usage
intF(s, res)
Arguments
s |
Vector of real numbers where the functions should be evaluated at. |
res |
An object of class |
Value
Vector of the same length as , containing the values of
at the elements of
.
Author(s)
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Lutz Duembgen, duembgen@stat.unibe.ch,
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html
References
Duembgen, L. and Rufibach, K. (2009) Maximum likelihood estimation of a log–concave density and its distribution function: basic properties and uniform consistency. Bernoulli, 15(1), 40–68.
Duembgen, L. and Rufibach, K. (2011) logcondens: Computations Related to Univariate Log-Concave Density Estimation. Journal of Statistical Software, 39(6), 1–28. doi:10.18637/jss.v039.i06
Rufibach K. (2006) Log-concave Density Estimation and Bump Hunting for i.i.d. Observations.
PhD Thesis, University of Bern, Switzerland and Georg-August University of Goettingen, Germany, 2006.
Available at https://slsp-ube.primo.exlibrisgroup.com/permalink/41SLSP_UBE/17e6d97/alma99116730175505511.
See Also
This function uses the output of activeSetLogCon
. The function intECDF
is similar, but based
on the empirical distribution function.
Examples
## estimate gamma density
set.seed(1977)
x <- rgamma(200, 2, 1)
res <- logConDens(x, smoothed = FALSE, print = FALSE)
## compute and plot the process D(t) in Duembgen and Rufibach (2009)
s <- seq(min(res$x), max(res$x), by = 10 ^ -3)
D1 <- intF(s, res)
D2 <- intECDF(s, res$xn)
par(mfrow = c(2, 1))
plot(res$x, res$phi, type = 'l'); rug(res$x)
plot(s, D1 - D2, type = 'l'); abline(h = 0, lty = 2)