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The hypotheses tests are implemented on the basis of two random effect or Bayesian models, namely, the hierarchical Poisson/Gamma or Negative Binomial model and the hierarchical Poisson/Lognormal model.
The figure represents the comparison results of ExOR protocol using simulation, binomial model, and the DTMC model for the comparison metric expected number of transmissions.
In ruin theory, the compound binomial model and the risk model based on a discrete-time renewal process have been extensively analyzed by [1, 2], among many others.
The timing hypothesis is tested using a Cox proportional hazard model, the pace hypothesis is tested using a random effects negative binomial model and the intensity hypothesis is tested using the random effects model.
This discrepancy between the negative binomial model and the variance to mean data was probably to be expected.
In Table 2, we present different estimations of a pooled proportion (event rates) using the binomial model and the beta-binomial model.
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We also obtain the score-type test statistics based on quasi-likelihoods using the mean-variance structure of the negative binomial model, and study the properties and performance characteristics of these.
We describe the statistical theories behind the beta-binomial model and the associated estimation methods.
We fitted the negative-binomial model and the hidden Markov chain using the steps recommended in the package vignette and the default parameters.
To quantify the variability between B and C, we defined the statistic as the ratio between the standard errors of the beta-binomial model and the binomial model (Section 3).
On the other hand, taken the precautions discussed in the paper, the log-binomial model and the Cox or Poisson models with adjusted variances provide correct point and interval estimates.
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