Order Statistics 1 Introduction and Notation

← Back to document page

Order Statistics 1 Introduction and Notation Let X1 , X2 , . . . , X10 be a random sample of size 15 from the uniform distribution over the interval (0, 1). Here are three different realizations realization of such samples. Because these samples come from a uniform distribution , we expect them to be spread out ran- domly and evenly across the interval (0, 1). (You might think that you are seeing some sort of clustering but keep in mind that you are looking at a measly selection of only three samples. After collecting more samples I'm sure your view would change!). Consider the single smallest value from each of these three samples, highlighted here. Collect the minimums onto a single graph. Not surprisingly, they are down towards zero! It would be pretty difficult to get a sample of 15. uniforms on (0, 1) that has a minimum up by the right endpoint of 1. In fact, we will show that if we kept collecting minimums of samples of size 15, they would have a probability density function that looks like this.

Order Statistics 1 Introduction and Notation Let X 1;X 2;:::;X 10 be a random sample of size 15 from the uniform distribution over the interval (0;1). Here are three di erent realizations realization of such samples. Because these samples come from a uniform distribution, we expect them to be spread out \ran-

  Introduction, Distribution, Statistics, Order, Notation, Order statistics 1 introduction and notation