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

Description

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

Details

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.

Author(s)

Kaspar Rufibach (maintainer) kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch
Fadoua Balabdaoui fadoua@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~fadoua
Hanna Jankowski hkj@mathstat.yorku.ca
http://www.math.yorku.ca/~hkj
Kathrin Weyermann

References

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.

Examples

1
## see the help files for the abovementioned functions for examples