rlogcon {logcondens}

Generate random sample from the log-concave and the smoothed log-concave density estimator

Description

Generate a random sample from a distribution with density \hat f_n and \hat f_n^*, as described in Duembgen and Rufibach (2009, Section 3).

Usage

rlogcon(n, x0)

Arguments

n

Size of random sample to be generated.

x0

Sorted vector of independent and identically distributed numbers, not necessarily unique.

Value

X

Random sample from \hat f_n.

X_star

Random sample from \hat f_n^*.

U

Uniform random sample of size n used in the generation of X.

Z

Normal random sample of size n used in the generation of X_star.

f

Computed log-concave density estimator.

f.smoothed

List containing smoothed log-concave density estimator, as output by evaluateLogConDens.

x

Vector of distinct observations generated from x0.

w

Weights corresponding to x.

Author(s)

Kaspar Rufibach, [e-mail],
http://www.kasparrufibach.ch

Lutz Duembgen, [e-mail],
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

Examples

## ===================================================
## Generate random samples as described in Section 3 of
## Duembgen and Rufibach (2009)
## ===================================================
x0 <- rnorm(111)
n <- 22
random <- rlogcon(n, x0)

## sample of size n from the log-concave density estimator
random$X

## sample of size n from the smoothed log-concave density estimator
random$X_star