Generate random sample from the log-concave and the smoothed log-concave density estimator
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).
rlogcon(n, x0)
n |
Size of random sample to be generated. |
x0 |
Sorted vector of independent and identically distributed numbers, not necessarily unique. |
X |
Random sample from \hat f_n. |
X_star |
Random sample from \hat f_n^*. |
U |
Uniform random sample of size |
Z |
Normal random sample of size |
f |
Computed log-concave density estimator. |
f.smoothed |
List containing smoothed log-concave density estimator, as output by |
x |
Vector of distinct observations generated from |
w |
Weights corresponding to |
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
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
## =================================================== ## 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
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