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q6_dev.R
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library(tidyverse)
theme_set(theme_bw())
library(latex2exp)
tibble(x = seq(-4, 4, by = .05),
y = dnorm(x)) -> q7_crit
q7_crit %>%
ggplot() +
geom_line(aes(x, y)) +
geom_area(data = q7_crit %>%
filter(x > 1.96),
aes(x, y),
fill = "red", alpha = .5) +
geom_area(data = q7_crit %>%
filter(x < -1.96),
aes(x, y),
fill = "red", alpha = .5) +
annotate(geom = "text", label = "???",
x = 2.3, y = 0.01) +
labs(x = "Statistics", y = "Density")
set.seed(123)
sost1 <- list()
for (i in 1:1000) {
sost1[[i]] <- rbeta(i, 5, 6)
}
names(sost1) <- 1:1000
sost1 %>%
map(mean) %>%
as_tibble() %>%
pivot_longer(cols = everything()) %>%
mutate(name = as.numeric(name)) %>%
ggplot(aes(name, value)) +
geom_line() +
geom_hline(yintercept = 5/(5+6),
size = 1,
color = "blue") +
annotate(geom = "text",
label = TeX("\\theta"),
x = 1005, y = 0.47,
color = "blue") +
labs(x = "n", y = TeX("$\\hat{\\theta}$"))
set.seed(123)
sost2 <- list()
for (i in 1:1000) {
sost2[[i]] <- rgamma(i, 1, 8)
}
names(sost2) <- 1:1000
sost2 %>%
map(mean) %>%
as_tibble() %>%
pivot_longer(cols = everything()) %>%
mutate(name = as.numeric(name)) %>%
ggplot(aes(name, value)) +
geom_line() +
geom_hline(yintercept = 0.2,
size = 1,
color = "blue") +
annotate(geom = "text",
label = TeX("\\theta"),
x = 1005, y = 0.21,
color = "blue") +
labs(x = "n", y = TeX("$\\hat{\\theta}$"))
set.seed(123)
sost3 <- list()
for (i in 1:1000) {
sost3[[i]] <- abs(rnorm(i, 1, 8) + rlnorm(i, 2, 2))
}
names(sost3) <- 1:1000
sost3 %>%
map(sum) %>%
as_tibble() %>%
pivot_longer(cols = everything()) %>%
mutate(name = as.numeric(name),
value = -log(value) + rnorm(1000, 0.5)) -> sost3.1
sost3.1 %>%
ggplot(aes(name, value)) +
geom_line() +
geom_hline(yintercept = -10.5,
size = 1,
color = "blue") +
annotate(geom = "text",
label = TeX("\\theta"),
x = 1010, y = -10,
color = "blue") +
labs(x = "n", y = TeX("$\\hat{\\theta}$"))
set.seed(123)
# sost4 <- list()
# for (i in 1:1000) {
# sost4[[i]] <- rnorm(i, 25, 25)
# }
# names(sost4) <- 1:1000
sost4 %>%
tibble(name = 1:1000,
value = rnorm(1000, 25, 10)) %>%
ggplot(aes(name, value)) +
geom_line() +
geom_hline(yintercept = 25,
size = 1,
color = "blue") +
annotate(geom = "text",
label = TeX("\\theta"),
x = 1020, y = 30,
color = "blue") +
labs(x = "n", y = TeX("$\\hat{\\theta}$")) +
ylim(-25, 100)
# q6_eff
ggplot() +
geom_function(fun = dnorm, args = list(mean = 0, 1.5),
color = "red3") +
geom_function(fun = dnorm, args = list(mean = 0, 2.4),
color = "blue3") +
geom_function(fun = dnorm, args = list(mean = -1.4, 0.7),
color = "green4") +
geom_function(fun = dnorm, args = list(mean = 1.2, 3),
color = "orange3") +
geom_vline(xintercept = 0, linetype = "dashed") +
annotate(geom = "text",
label = TeX("$\\theta$"),
x = .5, y = 0.4,
size = 5) +
annotate(geom = "text",
label = TeX("$\\theta_{1}$"),
x = -2.5, y = 0.4,
color = "green4", size = 5) +
annotate(geom = "text",
label = TeX("$\\theta_{2}$"),
x = 2.4, y = 0.2,
color = "red3", size = 5) +
annotate(geom = "text",
label = TeX("$\\theta_{3}$"),
x = -5, y = 0.05,
color = "blue3", size = 5) +
annotate(geom = "text",
label = TeX("$\\theta_{4}$"),
x = 5, y = 0.1,
color = "orange3", size = 5) +
xlim(-10, 10) +
labs(x = "Estimation", y = "Density")
library(tidyverse)
theme_set(theme_bw())
ggplot() +
geom_function(fun = dnorm) +
geom_function(fun = dnorm,
args = list(mean = .5,
sd = 2),
color = "red4") +
xlim(-5, 5)
moments::kurtosis(rnorm(100000, 0.5, 2)) - 3