Talk:Location parameter

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The definition shuold be expressed in terms of cumulative distribution functions. In the current form it is applicable to continuous distributions only. Moreover it seems to assume, the location parameter is the only one in the family of distributions. Olaf m (talk) 18:56, 4 April 2008 (UTC)Reply

You're right. I've expanded somewhat based on your comments. However, I think it is easier to understand the concept in terms of probability densities or probability mass functions, so I've used that terminology instead of cumulative distributions. --Zvika (talk) 07:09, 5 April 2008 (UTC)Reply

According to the article Summary statistics, the arithmetic mean (a central tendency) seems to be considered a location, which I guess indicates that there also is a location parameter for measuring the location. However, the definition given here (the equation) does not hold for any parameter that describes the Poisson distribution (for example), as that distribution only has one degree of freedom and changing the parameter that controls that degree (i.e. any of its central tendencies) not only shifts the distribution but reduces the height and the width of the "bump", which means that this equation doesn't hold for the Poisson distribution.

So, if the definition of location parameter given in this article is valid, that would mean that not all central tendencies can be considered location parameters and that there is a distinction between a location parameter and a central tendency. Is there such a distinction? Where does the definition come from? —Kri (talk) 13:57, 24 September 2018 (UTC)Reply

Before I list this at WP:AfD, does anyone want to add sources that establish this article meeting the requirements of WP:GNG? --Guy Macon (talk) 12:42, 17 May 2019 (UTC)Reply

Consider the distribution proportional to (x-a)^r-1(1-(x-a))^s-1 in the interval [a,a+1] and 0 outside it: would anyone say that it has a as a location parameter? The only reasonable location parameters are a+r/(r+s) and similar.

More generally, properties of distributions are not defined in terms of the formulae specifying them but in terms of their intrinsic behaviour.

My understanding of the notion of location and scale parameters is that they’re based on a loose concept of descriptions at varying levels of detail. You may say that data is gathered in the vicinity of m, or around m with a typical offset of s, or whatever; and a location parameter is suitably constructed if you can’t describe the data more accurately by improving on m but only by adding detail.

Google supports this view, eg. datatab, but I don’t have any reliable references. Colin.champion (talk) 07:24, 25 June 2021 (UTC)Reply

And although my proposed definition is informal, a formal property is implied by it. The location parameter of a point distribution is the location of the point. If a family of distributions approaches a point distribution (eg. (x-a)^r-1(1-(x-a))^2r-1 as r→∞) then its location parameters must approach this point. a+1/3 satisfies this property; a does not. Colin.champion (talk) 08:01, 25 June 2021 (UTC)Reply

Well, I took the plunge and tagged the article as ‘disputed accuracy’. It’s rather absurd that an article on such an elementary topic should cause problems, but no one can fix it without having access to relevant reliable sources. Perhaps an encyclopedia of statistics is the place to look. The datatab page is 100% accurate, though Wikipedia would want to pitch higher. Colin.champion (talk) 10:01, 1 July 2021 (UTC)Reply