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Just a note

For example, let us use Cn[x] to denote the cumulative distribution function (CDF) of our estimator - in other words, the proportion of estimates calculated from n observations which are less than some arbitrary value, x, ( P[<x] ).

In the special case of an unbiased, normalized, studentized, pivotal statistic, its cumulative distribution converges to standard normal ( Φ[x] ). - And because the normal distribution is continuous, for samples which approach infinity, the difference between observed and expected CDFs converges to zero ( |Cn[x] - Φ[x]|←0 ) - on average, at least. If the estimator is asymptotically biased , however, the difference would converge to that bias.