English

Accurate inference for a one parameter distribution based on the mean of a transformed sample

Methodology 2010-09-14 v1

Abstract

A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally O(n1/2)O(n^{-1/2}) and can be very considerable when the distribution is heavily biased or skew. This note shows how one may reduce this error to O(n(j+1)/2)O(n^{-(j+1)/2}), where jj is a given integer. The case considered is when the statistic is the mean of the sample values from a continuous one-parameter distribution, after the sample has undergone an initial transformation.

Keywords

Cite

@article{arxiv.1009.2190,
  title  = {Accurate inference for a one parameter distribution based on the mean of a transformed sample},
  author = {C. S. Withers and S. Nadarajah},
  journal= {arXiv preprint arXiv:1009.2190},
  year   = {2010}
}
R2 v1 2026-06-21T16:12:43.502Z