Posts tagged ‘distribution’

Guinness, Gosset, Fisher, and Small Samples

Student’s t-distribution is somewhat underrepresented in the astronomical community. Having an article with nice stories, it looks to me the best way to introduce the t distribution. This article describing historic anecdotes about monumental statistical developments occurred about 100 years ago.

Guinness, Gosset, Fisher, and Small Samples by Joan Fisher Box
Source: Statist. Sci. Volume 2, Number 1 (1987), 45-52.

No time for reading the whole article? I hope you have a few minutes to read following quotes, which are quite enchanting to me. Continue reading ‘Guinness, Gosset, Fisher, and Small Samples’ »

chi-square distribution [Eqn]

The Χ2 distribution plays an incredibly important role in astronomical data analysis, but it is pretty much a black box to most astronomers. How many people know, for instance, that its form is exactly the same as the γ distribution? A Χ2 distribution with ν degrees of freedom is

p(z|ν) = (1/Γ(ν/2)) (1/2)ν/2 zν/2-1 e-z/2 ≡ γ(z;ν/2,1/2) , where z=Χ2.

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[ArXiv] 5th week, Jan. 2008

Some statistics papers were listed at the top, of which topics would interest some slog subscribers.
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[ArXiv] 4th week, Jan. 2008

Only three papers this week. There were a few more with chi-square fitting and its error bars but excluded. Continue reading ‘[ArXiv] 4th week, Jan. 2008’ »

[ArXiv] Data-Driven Goodness-of-Fit Tests, Aug. 1, 2007

From arxiv/
Data-Driven Goodness-of-Fit Tests by L. Mikhail

Goodness-of-Fit tests have been essential in astronomy to validate the chosen physical model to observed data whereas the limits of these tests have not been taken into consideration carefully when observed data were put into the model for estimating the model parameters. Therefore, I thought this paper would be helpful to have a thought on the different point of views between the astronomers’ practice of goodness-of-fit tests and the statisticians’ constructing tests. (Warning: the paper is abstract and theoretical.)
Continue reading ‘[ArXiv] Data-Driven Goodness-of-Fit Tests, Aug. 1, 2007’ »