Comments on: Simple approximation to normal distribution http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/ The blog of John D. Cook Sat, 11 Feb 2012 22:42:11 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Links I’ve been thinking about « Belligerati http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-40616 Links I’ve been thinking about « Belligerati Wed, 23 Jun 2010 23:22:13 +0000 http://www.johndcook.com/blog/?p=5226#comment-40616 [...] just might have a use for a Simple approximation to normal distribution in my work on mortgage [...] [...] just might have a use for a Simple approximation to normal distribution in my work on mortgage [...]

]]> By: denis http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-38579 denis Mon, 17 May 2010 15:17:52 +0000 http://www.johndcook.com/blog/?p=5226#comment-38579 Another nice approximation is the piecewise-cubic M4 = M1 convolve M1 convolve M1 convolve M1 where M1(x) is the step function: 1 for x in -.5 .. .5, else 0. Explicitly, <code> def M4(x): return ( np.fmax( x+2, 0 ) ** 3 - 4 * np.fmax( x+1, 0 ) ** 3 + 6 * np.fmax( x, 0 ) ** 3 - 4 * np.fmax( x-1, 0 ) ** 3 + np.fmax( x-2, 0 ) ** 3 ) / 6 </code> This comes from a lovely paper by I.J.Schoenberg, "On equidistant cubic spline interpolation", Bulletin AMS, 1971. cheers -- denis Another nice approximation is the piecewise-cubic
M4 = M1 convolve M1 convolve M1 convolve M1
where M1(x) is the step function: 1 for x in -.5 .. .5, else 0.
Explicitly,

def M4(x):
return (
np.fmax( x+2, 0 ) ** 3
- 4 * np.fmax( x+1, 0 ) ** 3
+ 6 * np.fmax( x, 0 ) ** 3
- 4 * np.fmax( x-1, 0 ) ** 3
+ np.fmax( x-2, 0 ) ** 3
) / 6

This comes from a lovely paper by I.J.Schoenberg, “On equidistant cubic spline interpolation”, Bulletin AMS, 1971.

cheers
— denis

]]> By: Carnival of Mathematics #65 « Maxwell’s Demon http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-37898 Carnival of Mathematics #65 « Maxwell’s Demon Fri, 07 May 2010 17:39:51 +0000 http://www.johndcook.com/blog/?p=5226#comment-37898 [...] for more practical things, but to do this we often need to make approximations, for example of the normal distribution.  Code can also provide elegant ways to construct mathematical objects, such as a collection of [...] [...] for more practical things, but to do this we often need to make approximations, for example of the normal distribution.  Code can also provide elegant ways to construct mathematical objects, such as a collection of [...]

]]> By: Jan http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-37762 Jan Wed, 05 May 2010 05:48:20 +0000 http://www.johndcook.com/blog/?p=5226#comment-37762 Shucks... I tried to post images of these in the above. I know the first is correct. I believe the second, but I'm doing from memory. To see these, check out the links http://bilge.pyrate.mailbolt.com/blogBeginningFriendship7Day2010/PolyaGaussian.png and http://bilge.pyrate.mailbolt.com/blogBeginningFriendship7Day2010/AludaatAlodatGaussian.png Shucks… I tried to post images of these in the above. I know the first is correct. I believe the second, but I’m doing from memory. To see these, check out the links

http://bilge.pyrate.mailbolt.com/blogBeginningFriendship7Day2010/PolyaGaussian.png

and

http://bilge.pyrate.mailbolt.com/blogBeginningFriendship7Day2010/AludaatAlodatGaussian.png

]]> By: Jan http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-37761 Jan Wed, 05 May 2010 05:46:29 +0000 http://www.johndcook.com/blog/?p=5226#comment-37761 There's a history of these ... There's a famous approximation by Polya which I first learned of in the Chmura Kraemer and Thiemann book <em>How Many Subjects?</em>: and an improvement in, I believe, a Master's thesis by one Aludaat-Alodat: There’s a history of these … There’s a famous approximation by Polya which I first learned of in the Chmura Kraemer and Thiemann book How Many Subjects?:

and an improvement in, I believe, a Master’s thesis by one Aludaat-Alodat:

]]> By: Interesting Links - Statistics Teaching http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-37571 Interesting Links - Statistics Teaching Sun, 02 May 2010 13:28:02 +0000 http://www.johndcook.com/blog/?p=5226#comment-37571 [...] Approximation of the Normal Curve Using Cosine – John Cook at The Endeavour describes an approximation from an old paper in Psychometrika. This could be a nice exploration in a calculus or mathematical statistics course. [...] [...] Approximation of the Normal Curve Using Cosine – John Cook at The Endeavour describes an approximation from an old paper in Psychometrika. This could be a nice exploration in a calculus or mathematical statistics course. [...]

]]> By: vonjd http://www.johndcook.com/blog/2010/04/29/simple-approximation-to-normal-distribution/comment-page-1/#comment-37417 vonjd Fri, 30 Apr 2010 10:17:01 +0000 http://www.johndcook.com/blog/?p=5226#comment-37417 Another interesting paper in this context: http://www.jiem.org/index.php/jiem/article/download/60/27 Another interesting paper in this context:
http://www.jiem.org/index.php/jiem/article/download/60/27

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