Estimation of parameters. Maximum likelihood What has happened was most likely.

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Presentation transcript:

Estimation of parameters

Maximum likelihood What has happened was most likely

Examples

Binomial distribution Observations: k successes in N Bernoulli trials

Poisson distribution Observations: k 1, k 2, …, k N

Normal distribution Observations: X 1, X 2, …,X N

Exponential distribution Observations: X 1, X 2, …,X N

Moment estimators

For our examples moment estimators = maximum likelihood estimators

Are they always the same ? No

Uniform distribution Cauchy distribution

Unbiased and biased estimators

Variance of estimators minimum variance estimators

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