LCTLLRdistn: Limit Distribution of the Likelihood Ratio Statistic

Description Usage Format Details Source References See Also Examples


The LCTLLRdistn object gives the (estimated) limit distribution of Two times the log likelihood ratio for the location of the mode of a log-concave density f_0, under the assumption that f_0''(m)<0, where m is the mode of f_0.




LCTLLRdistn is an object with formal (S4) class 'distr' and subclass 'DiscreteDistribution' [package "distr"] with 12 slots. It is an estimate of a continuous limit distribution by a discrete one.


Gives the (discrete) support, i.e., the simulated values on which the estimate is based.


Formal class 'Reals' [package "distr"] with 2 slots




"Real Space"


NULL; unused slot.


function (n); simulates n values.


function (x, log = FALSE); constant 0 function.


function (q, lower.tail = TRUE, log.p = FALSE); the cumulative distribution function.


function (p, lower.tail = TRUE, log.p = FALSE); the quantile function.


logi FALSE; for internal use


logi FALSE; for internal use


logi FALSE; for internal use


logi TRUE; for internal use


Formal class 'NoSymmetry' [package "distr"] with 2 slots


character "non-symmetric distribution"




LCTLLRdistn is an object of class "distr" and subclass "DiscreteDistribution" from the package distr. The main uses are the three functions q (the quantile function), p (the cumulative distribution function) and r (which returns random samples). Note that d always returns 0 since the distribution is estimated discretely.

See the distr package for more details.


Obtained via simulation from a Gamma(3,1) distribution with density proportional to x^2 e^{-x} on (0,∞). We simulated the log likelihood ratio statistic 10^4 times, each time with a sample size of 1.2*10^3. The statistic was computed via the activeSetLogCon and activeSetLogCon.mode functions.


Duembgen, L, Huesler, A. and Rufibach, K. (2010) Active set and EM algorithms for log-concave densities based on complete and censored data. Technical report 61, IMSV, Univ. of Bern, available at

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.

Doss, C. R. (2013). Shape-Constrained Inference for Concave-Transformed Densities and their Modes. PhD thesis, Department of Statistics, University of Washington, in prepa- ration.

Doss, C. R. and Wellner, J. A. (2013). Inference for the mode of a log-concave density. Technical Report, University of Washington, in preparation.

See Also

See the "distr" package. The LRmodeTest and LCLRCImode functions use LCTLLRdistn.


LCTLLRdistn@q(.95); ##~1.06 is the 95% quantile

logcondens.mode documentation built on May 2, 2019, 8:26 a.m.