# rlogcon: Generate random sample from the log-concave and the smoothed... In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

## 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

 1 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, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

## 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. http://www.jstatsoft.org/v39/i06

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 ## =================================================== ## 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 

logcondens documentation built on May 2, 2019, 6:11 a.m.