The R Journal: accepted article

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A New Versatile Discrete Distribution PDF download
Rolf Turner

Abstract This paper introduces a new flexible distribution for discrete data. Approximate moment estimators of the parameters of the distribution, for use as starting values for a numerical maximum likelihood procedure, are discussed. The quality of the maximum likelihood estimates is assessed via simulation experiments. Several examples are given of fitting instances of the new distribution to real and simulated data. It is noted that the new distribution is a member of the exponential family. Expressions for the gradient and hessian of the log likelihood of the new distribution are derived. The former facilitates the numerical maximisation of the likelihood with optim(); the latter provides means of calculating or estimating the covariance matrix of of the parameter estimates. A discrepancy between estimates of the covariance matrix obtained by inverting the hessian and those obtained by Monte Carlo methods is discussed.

Received: 2021-01-15; online 2021-07-15
CRAN packages: hmm.discnp, rmutil, dbd, ellipse
CRAN Task Views implied by cited CRAN packages: Distributions, Multivariate


CC BY 4.0
This article is licensed under a Creative Commons Attribution 4.0 International license.

@article{RJ-2021-067,
  author = {Rolf Turner},
  title = {{A New Versatile Discrete Distribution}},
  year = {2021},
  journal = {{The R Journal}},
  doi = {10.32614/RJ-2021-067},
  url = {https://journal.r-project.org/archive/2021/RJ-2021-067/index.html}
}