diff --git a/vignettes/estimate_static_severity.Rmd b/vignettes/estimate_static_severity.Rmd index 74596669..be6f8af5 100644 --- a/vignettes/estimate_static_severity.Rmd +++ b/vignettes/estimate_static_severity.Rmd @@ -204,10 +204,10 @@ $$ where $f_t$ is the value of the probability mass function at time $t$, and $c_t$, $d_t$ are the number of new cases and new deaths at time $t$ (respectively). We then use $u_t$ in the following likelihood function to estimate severity. +$$ +{\sf L}(\theta | C_{t},D_{t},u_{t}) = \log \left(\binom{u_{t}C_{t}}{D_{t}}\right) + D_{t} \log \theta + (u_{t}C_{t} - D_{t}) \log (1 - \theta). $$ - {\sf L}(\theta | C_{t},D_{t},u_{t}) = \log{\dbinom{u_{t}C_{t}}{D_{t}}} + D_{t} \log{\theta} + - (u_{t}C_{t} - D_{t})\log{(1 - \theta)}, -$$ + $C_{t}$ and $D_{t}$ are the cumulative number of cases and deaths (respectively) until time $t$.