Author: Manuel Adrian Acuna-Zegarra; Andreu Comas-Garcia; Esteban Hernandez-Vargas; Mario Santana-Cibrian; Jorge X. Velasco-Hernandez
Title: The SARS-CoV-2 epidemic outbreak: a review of plausible scenarios of containment and mitigation for Mexico Document date: 2020_3_31
ID: aiq6ejcq_87
Snippet: The Negative Binomial distribution allows to control the variability of the data by considering over-dispersion which is common for epidemiological data. If α = 0, then we return to the Poisson model which is often used in this context. Let θ = (a, r, K, α) be the vector of parameters to estimate. The inclusion of the parameter α, which is related to the variability of the data, not to the Richards model, is necessary since in practice this v.....
Document: The Negative Binomial distribution allows to control the variability of the data by considering over-dispersion which is common for epidemiological data. If α = 0, then we return to the Poisson model which is often used in this context. Let θ = (a, r, K, α) be the vector of parameters to estimate. The inclusion of the parameter α, which is related to the variability of the data, not to the Richards model, is necessary since in practice this variability is unknown. Then, the likelihood function, which represent how likely is to observe the data under the Negative Binomial assumption and Richards model if we knew the parameters, is given by π(y 1 , . . . , y n |θ) = n j=1 Γ(y j + τ ) Γ(y j )Γ(τ ) τ τ + C(t j |a, r, K) τ C(t j |a, r, K) τ + C(t j |a, r, K)
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