Maximum likelihood for a binomial proportion
Section of Estimation, part of Statistical inference
Maximum likelihood for a binomial proportion
| Type | Section |
| Taught in | Estimation |
| Part | Statistical inference |
A single \operatorname{Bin}(n,p) count X=x has log-likelihood x\log p+(n-x)\log(1-p), up to a constant. The likelihood equation is
\frac xp-\frac{n-x}{1-p}=0,
so \widehat p=x/n, and the estimator is X/n. Maximum likelihood gives back the common-sense estimator.
Used in
- Taught in Estimation
- All 6 questions on Estimation
See also
Estimator · Method of moments · Sample correlation coefficient · Likelihood function · Maximum likelihood · Invariance of maximum likelihood · Unbiased estimator · Mean squared error