In a sample taken from a population, the kth order statistic is the kth smallest element in the sample. If we assume that the order of the elements in the sample is x1 < x2 < … < xn, then the kth order statistic, denoted x(k) is xk. Just as the mean can be treated as a random variable, we will also use the notation x(k) to represent a random variable.
Topics
- Distribution of Order Statistics from a Continuous Population
- Joint and Range Distribution from a Continuous Population
- Order Statistics for a Uniform Distribution
- Confidence Intervals for Order Statistics, Medians and Percentiles
- Distribution of Order Statistics from a Discrete Population
- Joint and Range Distribution from a Discrete Population
- Distribution of Order Statistics from a Finite Population
Click here for proofs that require calculus for various order statistic properties.
References
Chen, P-N (2008) Basic theories on order statistics
No longer available on the Internet
Omondi, O. C. (2016) Order statistics of uniform, logistic and exponential distributions
http://erepository.uonbi.ac.ke/bitstream/handle/11295/97307/MSc_Project2016.pdf?sequence=1&isAllowed=y
Ma D. (2010) The distribution of the order statistics. A Blog on probability and statistics
https://probabilityandstats.wordpress.com/2010/02/20/the-distributions-of-the-order-statistics/
Border, K. C. (2016) Lecture 15: Order statistics; conditional expectation. Caltech
https://healy.econ.ohio-state.edu/kcb/Ma103/Notes/Lecture15.pdf