Using the dataset Lahman::Batting
I've estimated parameters for the beta distribution. Now I want to plot this empirically derived beta distribution onto the histogram that I estimated it from.
library(dplyr)
library(tidyr)
library(Lahman)
career <- Batting %>%
filter(AB > 0) %>%
anti_join(Pitching, by = "playerID") %>%
group_by(playerID) %>%
summarize(H = sum(H), AB = sum(AB)) %>%
mutate(average = H / AB)
I can plot the distribution of RBI as:
career %>%
filter(AB > 500) %>%
ggplot(aes(x = average)) +
geom_histogram() +
geom_freqpoly(color = "red")
And obtain:
I know I can use + geom_freqpoly
to obtain:
But I want the smooth beta distribution. I can estimate beta parameters by:
career_filtered <- career %>%
filter(AB >= 500)
m <- MASS::fitdistr(career_filtered$average, dbeta,
start = list(shape1 = 1, shape2 = 10))
alpha0 <- m$estimate[1] # parameter 1
beta0 <- m$estimate[2] # parameter 2
Now that I have parameters alpha0
and beta0
, how do I plot the beta distribution so that I obtain something like this:
This question is based on a post I'm reading here.
All code, including the code for the plots, can be found here. The following code is used to get the requested plot:
ggplot(career_filtered) +
geom_histogram(aes(average, y = ..density..), binwidth = .005) +
stat_function(fun = function(x) dbeta(x, alpha0, beta0), color = "red",
size = 1) +
xlab("Batting average")
Hope this helps.