0

this wiki page says

Consider a case where n tickets numbered from 1 to n are placed in a box and one is selected at random; thus, the sample size is 1. If n is unknown, then the maximum likelihood estimator $\widehat {n}$ of n is the number m on the drawn ticket. (The likelihood is 0 for n < m, ​1⁄n for n ≥ m, and this is greatest when n = m.

there are 3 cases.

case_1: 0 for n < m means this case never happens, which is reasonable.

case_2: n ≥ m, 1⁄20 for n ≥ m is reasonable since the numbers follow the discrete uniform distribution.

case_3: n = m, "this is greatest". what does that mean?

Could someone give an example to illustrate this?

JJJohn
  • 1,436

1 Answers1

1

The likelihood, a function of the unknown parameter $n$, has turned out to be $1/n$ for $n \geq m$ and zero elsewhere. This is maximized at $n=m$, so the MLE is $m$. For example, had you picked 5, the probability of you picking 5 is higher assuming $n=5$ (probability 1/5) than, say, $n=20$ (probability 1/20).

Juno Kim
  • 610