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Is it valid to assume that all errors follow the uniform (rectangular) distribution?

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Is it valid to assume that all errors follow the uniform (rectangular) distribution?

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No. The uniform distribution applies only to a very small fraction of measurement errors. Chief among these are errors due to digital readout resolution and phases of detected electromagnetic signals. In general, you must consider which distribution is applicable for each error source. It is never a recommended practice to use a one-distribution-fits-all-errors approach.

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