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What is the minimum-variance unbiased estimator for a uniform distribution?

Given a uniform distribution on [0, b] with unknown b, the minimum-variance unbiased estimator (UMVUE) for the maximum is given by. where m is the sample maximum and k is the sample size, sampling without replacement (though this distinction almost surely makes no difference for a continuous distribution).

What is a continuous uniform distribution?

Uniform distribution (continuous) In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

What is a consistent estimator?

In this way one would obtain a sequence of estimates indexed by n, and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value θ 0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent.

What is the probability density function of uniform distribution?

The probability density function of the continuous uniform distribution is: The values of f ( x) at the two boundaries a and b are usually unimportant because they do not alter the values of the integrals of f(x) dx over any interval, nor of x f(x) dx or any higher moment. Sometimes they are chosen to be zero, and sometimes chosen to be 1 b − a.

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