# 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
``` |

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