add distribution plot and spoiler on method

episodes/severity-static.Rmd

@@ -237,7 +237,7 @@ Answer to these questions:
 
 ## Delay-adjusted CFR
 
-[Nishiura et al., 2009](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0006852) developed a method that considers the time delay from the onset of symptoms to death.
+[Nishiura et al., 2009](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0006852) developed a method that considers the **time delay** from the onset of symptoms to death.
 
 Real-time outbreaks may have a number of deaths that are insufficient to determine the time distribution between onset and death. Therefore, we can estimate the _distribution delay_ from historical outbreaks or reuse the ones available in systematic reviews from repositories like `{epiparameter}` or `{epireview}`.
 
@@ -251,8 +251,37 @@ onset_to_death_ebola <-
     epi_dist = "onset_to_death",
     single_epidist = TRUE
   )
+
+# Plot <epidist> object
+plot(onset_to_death_ebola, day_range = 0:40)
 ```
 
+::::::::::::::::::::::::::: spoiler
+
+### How does {cfr} works?
+
+To adjust the CFR, [Nishiura et al., 2009](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0006852) use the case and death incidence data to estimate the number of cases with known outcomes:
+
+$$
+  u_t = \dfrac{\sum_{i = 0}^t
+        \sum_{j = 0}^\infty c_{i - j} f_{j}}{\sum_{i = 0} c_i},
+$$
+
+where 
+- $c_{t}$ is the daily case incidence at time, $t$, 
+- $f_{t}$ is the value of the probability mass function of the **delay distribution** between onset and death. 
+- $u_{t}$ represents the underestimation of the known outcomes and is used to **scale** the value of the cumulative number of cases in the denominator in the calculation of the CFR.
+
+The [`estimate_outcomes()`](https://epiverse-trace.github.io/cfr/reference/estimate_outcomes.html) function is used internally to calculate $u_{t}$.
+
+The estimator for CFR can be written as: 
+
+$$p_{t} = b_{t} / u_{t}$$
+
+where $p_{t}$ is the realized proportion of confirmed cases to die from the infection (or the unbiased CFR), and $b_{t}$, the crude and biased estimate of CFR (also naive CFR).
+
+:::::::::::::::::::::::::::
+
 To calculate the delay-adjusted CFR, we can use the `cfr_static()` function with the `data` and `delay_density` arguments.
 
 ```{r}