Handouts
Week14:
CRLB
Normal MLE, parametric and nonparametric bootstrap of the mean.
- normal_basic.r percentile bootstrap and method presented in the book (basic).
- normal_para.r nonparametric bootstrap using the boot function.
Nonparametric Bootstrap.
Confidence Intervals
- Spotlight R Notebook: Simulated Confidence Intervals
- Spotlight R package: pwrss
Simulation of the confidence level
Power and Effect Size
Likelihood Ratio Test examples
Distribution of the p-value under the null hypothesis.
Week13:
Large Sample Theory of the MLE
Using the R package fitdistrplus to fit models to a random sample.
- mle.normal.fitdistrplus.html
- mle.normal.fitdistrplus.qmd
- mle.gamma.fitdistrplus.html
- mle.gamma.fitdistrplus.qmd
Week12:
Fitting models to a random sample.
Using the R package fitdistrplus to fit models to a random sample.
MLEs
Week10:
- Ch. 7 Survey Sampling has been posted
- Confidence Intervals
Week09:
- Prediction
- Simulation of the Sampling Distributions of order statistics:
Week08:
- Limit Theorems:
Week07:
- Sums of random variables:
- Chebyshev’s Inequality, first approximate CI
Week06:
- Order Statistics
- order_statistics.pdf
- ChatGPT generated version of my handout. I uploaded my handwritten .pdf file to ChatGPT and asked it to create a R Quarto Notebook from my handwritten notes. Note that it corrected a few small math errors.
- order_statistics_ver03.html
- order_statistics_ver03.pdf
- order_statistics_ver03.qmd
- Shared Chat ChatGPT link
Week05:
- Normal random number generation
- box_muller.pdf
- ChatGPT generated version of my handout with some additional explanation. I uploaded my handwritten .pdf file to ChatGPT and asked it to create a R Quarto Notebook from my handwritten notes and to generate a more detailed explanation of the Box-Muller algorithm. Note that it corrected the math error I pointed out in class.
- box_muller_ver07.html
- box_muller_ver07.pdf
- box_muller_ver07.qmd
- Shared Chat ChatGPT link
Week04:
- R p,d,q, and r
- Conditional Probability Example: Particle Counter
Week03:
- Class Handouts:
- Transformation of uniform random numbers. Use of the quantile function.
Week02:
Class Handouts:
Introduction to R. IntroductionR.pdf
Birthday Problem Stats Magazine Paper. Birthday.pdf
Examples:
- Introduction to simulation in R. example1.r
- Introduction to graphics in R. example2.r
- RANDU example3a.r
Please take look at the following Handouts on random number generation.
- handout1.pdf Generating Pseudo-random Numbers
- handout2.pdf Simulation Example
- handout3.pdf Simulating Discrete Random Variables
- handout4.pdf Simulating Normal Pseudo-random Numbers