Editing Truncated mean (section)

==Advantages==
The truncated mean is a useful estimator because it is less sensitive to [[outlier]]s than the mean but will still give a reasonable estimate of central tendency or mean for many statistical models. In this regard it is referred to as a [[Robust statistics|robust estimator]]. For example, in its use in Olympic judging, truncating the maximum and minimum prevents a single judge from increasing or lowering the overall score by giving an exceptionally high or low score.

One situation in which it can be advantageous to use a truncated mean is when estimating the [[location parameter]] of a [[Cauchy distribution]], a bell shaped probability distribution with (much) fatter tails than a [[normal distribution]].  It can be shown that the truncated mean of the middle 24% sample [[order statistics]] (i.e., truncate the sample by 38% at each end) produces an estimate for the population location parameter that is more efficient than using either the sample median or the full sample mean.<ref name=rothenberg>{{cite journal|last1=Rothenberg|first1=Thomas J.|last2=Fisher|first2=Franklin, M.|last3=Tilanus|first3=C.B.|year=1964|volume=59|issue=306|journal=Journal of the American Statistical Association|title=A note on estimation from a cauchy sample|pages=460–463|doi=10.1080/01621459.1964.10482170}}</ref><ref name=bloch>{{cite journal|last1=Bloch|first1=Daniel|year=1966|volume=61|issue=316|journal=Journal of the American Statistical Association|title=A note on the estimation of the location parameters of the Cauchy distribution|pages=852–855|jstor=2282794|doi=10.1080/01621459.1966.10480912}}</ref> However, due to the fat tails of the Cauchy distribution, the efficiency of the estimator decreases as more of the sample gets used in the estimate.<ref name=rothenberg/><ref name=bloch/>  Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a [[maximum likelihood]] estimator, nor are any as asymptotically efficient as the maximum likelihood estimator; however, the maximum likelihood estimate is more difficult to compute, leaving the truncated mean as a useful alternative.<ref name=bloch/><ref name=ferguson>{{cite journal|last1=Ferguson|first1=Thomas S.|author-link= Thomas S. Ferguson |year=1978|journal=Journal of the American Statistical Association |volume=73|issue=361|title=Maximum Likelihood Estimates of the Parameters of the Cauchy Distribution for Samples of Size 3 and 4|pages=211–213|jstor=2286549|doi=10.1080/01621459.1978.10480031}}</ref>