Talk:Minimum-distance estimation
Latest comment: 15 years ago by Avraham in topic Population Distribution
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Population Distribution edit
This population distribution , what is its domain and range? I know it says that with , but where does x live, and where does live? It might look nice if it were to be written explicitly, like: where the spaces X and Y need to be given.
Declan Davis (talk) 19:17, 24 September 2008 (UTC)
- Goodness, I'm just a lowly actuary, when you say spaces I think of the QWERTY keyboard . Seriously, I'm not 100% certain as to the space of . Drossos & Phillippou did not explicitly state it, as they did for . Although they do discuss as a class of distribution functions and define as being defined on .
- Kim & Lee (1999) describe the distance without referring to the population of at all, talking solely about the space of .
- Anderson & Darling (1952) define . -- Avi (talk) 19:38, 24 September 2008 (UTC)
- From my foray through the literature, I do not see why the samples need to be one-dimensional, although they almost always are, so seems reasonable for the domain and range of as well. has to live on the closed interval between 0 and 1, of course, as it is a distribution function. I do hope someone more erudite in this area than I drops by, though. -- Avi (talk) 00:41, 25 September 2008 (UTC)
- I'm not an expert, but I'll try to explain it. is a statistical model. The set is a parameter space and theoretically it could be any non-empty set. In practice parameters are real numbers and where n is the number of parameters. Each function is probability distribution. The range of is closed interval [0,1]. If the random samples are in the sample space X, then domain of each is X (or the set of all measurable subsets of X). Usually X is either the set of real number or the set of integers (or subset of either). Tlepp (talk) 08:33, 26 September 2008 (UTC)