Problem 1

studio10_problem_1(0, 1, 400, 500, 500, 0.95)
## 
## ----------------------------------
## Problem 1: Simulated type 1 empirical bootstrap CI error rate: normal distribution
## Normal: true mean = 0 true_median = 0 true_sd = 1 n_data = 400 n_boot = 500 n_trials = 500 confidence = 0.95 
## Nominal confidence: 0.95 
## Type 1 error rates (percentile, basic):
##   mean: 0.058 0.058 
##   median: 0.042 0.084 
##   sd: 0.06 0.05
studio10_problem_1(1, 1.5, 200, 1000, 2000, 0.9)
## 
## ----------------------------------
## Problem 1: Simulated type 1 empirical bootstrap CI error rate: normal distribution
## Normal: true mean = 1 true_median = 1 true_sd = 1.5 n_data = 200 n_boot = 1000 n_trials = 2000 confidence = 0.9 
## Nominal confidence: 0.9 
## Type 1 error rates (percentile, basic):
##   mean: 0.103 0.0985 
##   median: 0.082 0.1585 
##   sd: 0.111 0.107

Problem 2

Problem 2a

studio10_problem_2a(0, 1)
## 
## ----------------------------------
## Problem 2a: Print true mean and true std of the log normal distribution
## LogNormal: meanlog=0.0, sdlog=1.0 
## Distribution mean=1.65, median=1.00, std dev=2.16
studio10_problem_2a(0, 2)
## 
## ----------------------------------
## Problem 2a: Print true mean and true std of the log normal distribution
## LogNormal: meanlog=0.0, sdlog=2.0 
## Distribution mean=7.39, median=1.00, std dev=54.10
studio10_problem_2a(-3, 1.5)
## 
## ----------------------------------
## Problem 2a: Print true mean and true std of the log normal distribution
## LogNormal: meanlog=-3.0, sdlog=1.5 
## Distribution mean=0.15, median=0.05, std dev=0.45
studio10_problem_2a(-2, 1)
## 
## ----------------------------------
## Problem 2a: Print true mean and true std of the log normal distribution
## LogNormal: meanlog=-2.0, sdlog=1.0 
## Distribution mean=0.22, median=0.14, std dev=0.29

Problem 2b

studio10_problem_2b(0, 1, 100, 500, 1000, 0.95)
## -----
## Problem 2b: Simulated type 1 empirical bootstrap CI error rate: log normal distribution
## LogNormal: meanlog=0.0, sdlog=1.0 
## Distribution mean=1.65, median=1.00, std dev=2.16 
## n_data = 100 n_boot = 500 n_trials = 1000 
## Nominal confidence: 0.95 
## Type 1 error rates (percentile, basic):
##   mean: 0.09 0.109 
##   median: 0.068 0.103 
##   sd: 0.321 0.309
studio10_problem_2b(-3, 1.5, 50, 2000, 1000, 0.9)
## -----
## Problem 2b: Simulated type 1 empirical bootstrap CI error rate: log normal distribution
## LogNormal: meanlog=-3.0, sdlog=1.5 
## Distribution mean=0.15, median=0.05, std dev=0.45 
## n_data = 50 n_boot = 2000 n_trials = 1000 
## Nominal confidence: 0.9 
## Type 1 error rates (percentile, basic):
##   mean: 0.228 0.261 
##   median: 0.096 0.215 
##   sd: 0.682 0.656
studio10_problem_2b(-2, 1, 200, 600, 1000, 0.8)
## -----
## Problem 2b: Simulated type 1 empirical bootstrap CI error rate: log normal distribution
## LogNormal: meanlog=-2.0, sdlog=1.0 
## Distribution mean=0.22, median=0.14, std dev=0.29 
## n_data = 200 n_boot = 600 n_trials = 1000 
## Nominal confidence: 0.8 
## Type 1 error rates (percentile, basic):
##   mean: 0.214 0.208 
##   median: 0.205 0.273 
##   sd: 0.391 0.406

MIT OpenCourseWare

https://ocw.mit.edu

18.05 Introduction to Probability and Statistics

Spring 2022

Authors: Jeremy Orloff and Jennifer French

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