For a Uniform[0,θ] model, the maximum-likelihood estimate is the sample maximum, while the moment estimate is twice the sample mean. These two estimates need not agree because they are derived from different principles: the likelihood depends on the support covering every observation, whereas the moment estimate relies on the expected value.
Conditions: The model is Uniform[0,θ].; The parameter θ is positive.; Admissible parameter values must cover every observation.
For a Uniform[0,θ] model, the maximum-likelihood estimate is the sample maximum, while the moment estimate is twice the sample mean. These two estimates need not agree because they are derived from different principles: the likelihood depends on the support covering every observation, whereas the moment estimate relies on the expected value.
Conditions: The model is Uniform[0,θ].; The parameter θ is positive.; Admissible parameter values must cover every observation.