Create Assignment1

LinaKramer/Assignment1

@@ -0,0 +1,2 @@
+Utrecht
+2022

LinaKramer/Assignment1.Rmd

@@ -0,0 +1,70 @@
+---
+title: "Monte Carlo simulation (exercise1)"
+author: "Lina Kramer"
+date: "9/14/2022"
+output: html_document
+---
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE)
+```
+
+```{r}
+library(future)
+library(furrr)
+library(dplyr)
+library(magrittr)
+```
+
+```{r}
+
+nsim = 100 # 100 samples
+plan(multisession)
+
+# start future mapping
+SIM <- future_map(1:nsim, function(x){
+  x <- rnorm(5000, mean = 0, sd = 1)
+  M <- mean(x)
+  DF <- length(x) - 1
+  SE <- 1 / sqrt(length(x))
+  INT <- qt(.975, DF) * SE
+  return(c(mean = M, 
+           bias = M - 0, 
+           std.err = SE, 
+           lower = M - INT, 
+           upper = M + INT, 
+           cov = M - INT < 0 & 0 < M + INT))
+}, 
+.options = furrr_options(seed = 123), 
+.progress = TRUE) %>% 
+  do.call("rbind", args = .) %>% 
+  as_tibble
+
+
+```
+
+```{r}
+SIM %>% colMeans
+```
+```{r}
+SIM %>% filter(!cov)
+```
+
+```{r}
+library(DT)
+SIM %>% 
+  round(4) %>% 
+  datatable()
+```
+
+```{r}
+library(ggplot2)
+limits <- aes(ymax = SIM$upper, ymin = SIM$lower)
+SIM %>% mutate(covered = as.factor(cov)) %>% 
+ggplot(aes(y=mean, x=1:100, colour = covered)) + 
+  geom_hline(aes(yintercept = 0), color = "dark grey", size = 2) + 
+  geom_pointrange(limits) + 
+  xlab("Simulations 1-100") +
+  ylab("Means and 95% Confidence Intervals")
+```
+