Estimation of parameters

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Estimation of parameters
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Maximum likelihood

• What has happened was most likely

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Examples
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Binomial distribution
Observations k successes in N Bernoulli trials
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Poisson distribution
Observations k1, k2, , kN
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Normal distribution
Observations X1, X2, ,XN
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Exponential distribution
Observations X1, X2, ,XN
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Moment estimators
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For our examples moment estimators maximum
likelihood estimators
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Are they always the same ?
No
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Uniform distributionCauchy distribution
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Unbiased and biased estimators
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Variance of estimatorsminimum variance estimators