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Table 3 Word count model comparisons

From: A flexible distribution class for count data

  CMP/sCMP(m=1) sCMP(m=2) sCMP(m=3) sCMP(m=4)
\(\hat {\lambda }\) (SE) 1.8897 (0.4219) 0.9120 (0.1511) 0.5385 (0.0652) 0.3559 (0.0404)
\(\hat {\nu }\) (SE) 2.1033 (0.3858) 3.7750 (1.0049) 3.0900 (15045) 29.7650 (13118)
log(L) -118.319 -117.327 -117.331 -118.521
AIC 240.638 238.655 238.662 241.041
BIC 245.848 243.865 243.873 246.252
  1. Model comparison for the word count data from Bailey (1990), where sCMP with m=1,2,3,4 distributions are considered. For model comparisons, the log-likelihood, Akaike and Bayes Information Criterions (AIC and BIC, respectively) are provided. All sCMP family distributions outperform the Poisson model which produces an estimated sample mean, μ =1.0500 (0.1025), with log-likelihood − 123.2741. The negative binomial model likewise converges to a Poisson model with estimates, \(\hat {\theta } = 269.9607\) (702.1046), \(\hat {\mu }=1.0500\) (0.1027), log(L)=−123.3487)