Order Statistics

Learn about order statistics in this comprehensive 2.5-hour tutorial. Explore summation formulas for integers, convergence of nth order statistics from uniform to exponential distributions, and derive joint probability density functions for order statistics. Dive into discrete order statistics with R illustrations, construct confidence intervals for population medians using sample order statistics, and create QQ-plots and rankit plots. Understand the Shapiro-Wilk normality test, moments of order statistics from uniform distributions, and joint distributions of mid-range and range. Gain practical skills in statistical analysis and data interpretation through hands-on examples and R programming.

Summation Formulas for Integers.
Nth Order Statistic from a Uniform Converges in Distribution to an Exponential.
Transformations: Derive the Joint pdf of Order Statistics.
Discrete Order Statistics with Illustration using R.
Using R for a 95% CI for Population Median using Sample Order Statistics.
CI for Population Median using Order Statistics.
Using R: QQ-Plots versus Rankit Plots..
Using R: Shapiro-Wilk Normality Test.
Moments of Order Statistics from a Unif[0,1] Distribution.
Joint Distribution of the Mid-Range and the Range.