| | 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 |
- 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)
