Other Examples
- For a normal distribution with unknown mean and variance, the sample mean and (unbiased) sample variance are the MVUEs for the population mean and population variance.
- However, the sample standard deviation is not unbiased for the population standard deviation – see unbiased estimation of standard deviation.
- Further, for other distributions the sample mean and sample variance are not in general MVUEs – for a uniform distribution with unknown upper and lower bounds, the mid-range is the MVUE for the population mean.
- If k exemplars are chosen (without replacement) from a discrete uniform distribution over the set {1, 2, ..., N} with unknown upper bound N, the MVUE for N is
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- where m is the sample maximum. This is a scaled and shifted (so unbiased) transform of the sample maximum, which is a sufficient and complete statistic. See German tank problem for details.
Read more about this topic: Minimum-variance Unbiased Estimator
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