>
>"In most cases, as in the case of errors of observation, they have a fairly
>definite symmetrical shape and one that approaches with a close degree of
>approximation to the well-known error or probability-curve. A frequency
>curve, which, for practical purposes, can be represented by the error curve,
>will for the remainder of this paper be termed a "normal curve". When a series
>of measurements gives rise to a normal curve, we may probably assume something
>approaching a stable condition; there is production and destruction
>impartially
>around the mean."
>
>Karl Pearson, Contributions to the mathematical theory of evolution, Phil.
>Trans. Royal Soc. London, A, 185, 1894, 71-110.
>
>Clearly "normal" is meant normatively, in the sense that skew variation
>is abnormal. This is very much in the tradition of Quetelet
>and his "average man". Also clearly, Pearson later changed his mind
>(somewhat).
>
>
>>Hi Jan,
>>
>>I have always understood that the word 'normal' in this context means
>>'perpendicular'. You might remember calculus exercises in which you
>>were asked
>>to find 'the equation to the normal to a curve', just after you were asked to
>>find the equation to the tangent.
>>
>>The reason why this name applies is because of the orthogonality
>>properties of
>>the (multi)normal distribution.
>>
>>If you take a simple random sample from a normal distribution, and represent
>>each Xi by a different axis, the axes will be mutually perpendicular.
>>
>>Obviously there is more to it than this, but I can't remember the
>>details. But
>>you should be able to chase it up.
>>
>>Regards,
>>Alan
>>
>>Jan Souman wrote:
>>
>>> Does anybody know why the normal distribution is called 'normal'? The most
>>> plausible explanations I've encountered so far are:
>>>
>>> 1. The value of a variable that has a normal distribution is determined by
>>> many different factors, each contributing a small part of the total value.
>>> Because this is the case with many real life variables, like length and
>>> intelligence, the resulting distribution of values is called normal.
>>>
>>> 2. Many probability distributions are approximated by the normal
>>> distribution for large sample sizes.
>>>
>>> Maybe there are other explanations and maybe someone knows the
>>>source of the
>>> name?
>>>
>>> Jan Souman
>>> Dpt. of Social Sciences
>>> University of Utrecht, Netherlands
>>>
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>>
>>--
>>Alan McLean ([EMAIL PROTECTED])
>>Department of Econometrics and Business Statistics
>>Monash University, Caulfield Campus, Melbourne
>>Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
>>
>>
>>
>>
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--
===
Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
US mail: 8142 Math Sciences Bldg, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550; fax (310)-206-5658; email: [EMAIL PROTECTED]
http://www.stat.ucla.edu/~deleeuw and http://home1.gte.net/datamine/
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