Warning: package 'ggplot2' was built under R version 4.5.2
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
✔ forcats 1.0.0 ✔ stringr 1.5.1
✔ ggplot2 4.0.1 ✔ tibble 3.3.0
✔ lubridate 1.9.4 ✔ tidyr 1.3.1
✔ purrr 1.1.0
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
Attaching package: 'purrrfect'
The following objects are masked from 'package:base':
replicate, tabulate
sim_data <- parameters(~n, c(4, 8, 12, 16)) %>%
add_trials(10000) %>%
mutate(
y_sample = pmap(list(n), function(n) sort(runif(n))),
y_1 = map_dbl(y_sample, 1),
y_3 = map_dbl(y_sample, 3),
y_n = map_dbl(y_sample, tail, 1),
f_1 = dbeta(y_1, 1, n),
f_3 = dbeta(y_3, 3, n - 2),
f_n = dbeta(y_n, n, 1)
)
ggplot(sim_data, aes(x = y_1)) +
geom_histogram(aes(y = after_stat(density)), fill = 'goldenrod', bins = 40) +
geom_line(aes(y = f_1), col = 'cornflowerblue', size = 1) +
facet_wrap(~n, scales = "free_y", labeller = label_both) +
theme_classic() +
labs(title = "Y(1) Order Statistic")
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
ggplot(sim_data, aes(x = y_3)) +
geom_histogram(aes(y = after_stat(density)), fill = 'goldenrod', bins = 40) +
geom_line(aes(y = f_3), col = 'cornflowerblue', size = 1) +
facet_wrap(~n, scales = "free_y", labeller = label_both) +
theme_classic() +
labs(title = "Y(3) Order Statistic")
ggplot(sim_data, aes(x = y_n)) +
geom_histogram(aes(y = after_stat(density)), fill = 'goldenrod', bins = 40) +
geom_line(aes(y = f_n), col = 'cornflowerblue', size = 1) +
facet_wrap(~n, scales = "free_y", labeller = label_both) +
theme_classic() +
labs(title = "Y(n) Order Statistic")
