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Let X1, X2, ..., Xn be a random sample from a distribution with density:
f(x) = x1 x (0, 1) 0 otherwise
where > 0 is an unknown parameter. Find the method of moments and method of quantiles
estimators for (based on the mean and median, respectively) and the m.l.e. of . Compare the
values of the three estimators for a sample consisting of the following three observations: 1/3 ,
1/2 , 5/6 .

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Estimating Parameter of Uniform Distribution from Sample Mean, Median, MLE

  • 1. Let X1, X2, ..., Xn be a random sample from a distribution with density: f(x) = x1 x (0, 1) 0 otherwise where > 0 is an unknown parameter. Find the method of moments and method of quantiles estimators for (based on the mean and median, respectively) and the m.l.e. of . Compare the values of the three estimators for a sample consisting of the following three observations: 1/3 , 1/2 , 5/6 .