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.
1 |
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
1
"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"
NULL
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 http://arxiv.org/abs/0707.4643.
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
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 the "distr" package. The LRmodeTest
and
LCLRCImode
functions use LCTLLRdistn.
1 | LCTLLRdistn@q(.95); ##~1.06 is the 95% quantile
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