Estimate a Log-Concave Probability Mass Function from Discrete i.i.d. Observations


Implements the maximum likelihood estimator (MLE) for a probability mass function (PMF) under the assumption of log-concavity from i.i.d. data.


Package: logcondiscr
Type: Package
Version: 1.0.6
Date: 2015-07-03
License: GPL (>=2)
LazyLoad: yes

The main functions in the package are:

logConDiscrMLE: Compute the maximum likelihood estimator (MLE) of a log-concave PMF from i.i.d. data. The constrained log-likelihood function is maximized using an active set algorithm as initially described in Weyermann (2007).

logConDiscrCI: Compute the maximum likelihood estimator (MLE) of a log-concave PMF from i.i.d. data and corresponding, asymptotically valid, pointwise confidence bands as developed in Balabdaoui et al (2012).

kInflatedLogConDiscr: Compute an estimate of a mixture of a log-concave PMF that is inflated at k, from i.i.d. data, using an EM algorithm.


Kaspar Rufibach (maintainer)
Fadoua Balabdaoui
Hanna Jankowski
Kathrin Weyermann


Balabdaoui, F., Jankowski, H., Rufibach, K., and Pavlides, M. (2013). Maximum likelihood estimation and confidence bands for a discrete log-concave distribution. J. R. Stat. Soc. Ser. B Stat. Methodol., 75(4), 769–790.

Weyermann, K. (2007). An Active Set Algorithm for Log-Concave Discrete Distributions. MSc thesis, University of Bern (Supervisor: Lutz Duembgen).

See Also

Functions to estimate the log-concave MLE for a univariate continuous distribution are provided in the package logcondens and for observations in more than one dimension in LogConDEAD.


## see the help files for the abovementioned functions for examples