Editing Talk:2118: Normal Distribution
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Just to say, Randall's horizontal slice isn't entirely meaningless. It's a calculation I've had to do, where I have a series of binned samples of a population (say I knew how many fell in -10..10, how many fell in -5..5, how many fell in -2..2) and wanted to combine them with an appropriate weighting to approximate a Gaussian. I was using it for filtering, but it's logically similar. [[User:Fluppeteer|Fluppeteer]] ([[User talk:Fluppeteer|talk]]) 16:19, 1 March 2019 (UTC) | Just to say, Randall's horizontal slice isn't entirely meaningless. It's a calculation I've had to do, where I have a series of binned samples of a population (say I knew how many fell in -10..10, how many fell in -5..5, how many fell in -2..2) and wanted to combine them with an appropriate weighting to approximate a Gaussian. I was using it for filtering, but it's logically similar. [[User:Fluppeteer|Fluppeteer]] ([[User talk:Fluppeteer|talk]]) 16:19, 1 March 2019 (UTC) | ||
− | ::Also, the slice sampler for MCMC is a trick for sampling from a distribution by "turning it on its side". But I don't think the 50% figure would be meaningful in that context. | + | ::Also, the slice sampler for MCMC is a trick for sampling from a distribution by "turning it on its side". But I don't think the 50% figure would be meaningful in that context. [[Special:Contributions/172.68.54.136|172.68.54.136]] 21:16, 1 March 2019 (UTC) |
Pedant: etymologically, there *is* actually a connection between a normal (to a surface or line) and the normal distribution; the former comes from the Latin for a set square (giving you perpendicular), and it later came to mean "standard". The "tangential distribution" certainly fits the etymology of "odd/unusual" though. [[User:Fluppeteer|Fluppeteer]] ([[User talk:Fluppeteer|talk]]) 16:26, 1 March 2019 (UTC) | Pedant: etymologically, there *is* actually a connection between a normal (to a surface or line) and the normal distribution; the former comes from the Latin for a set square (giving you perpendicular), and it later came to mean "standard". The "tangential distribution" certainly fits the etymology of "odd/unusual" though. [[User:Fluppeteer|Fluppeteer]] ([[User talk:Fluppeteer|talk]]) 16:26, 1 March 2019 (UTC) | ||
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Say I want to build a diverse team or a representative council. And it is more important that the selection is representative of several subpopulations (who should not be voted down by the majority) than that it gives an equal fair chance to anybody. I would cut away the absolute outliers and reduce the weight of the most abundant group - this gives just the area between the two lines. Sebastian --[[Special:Contributions/172.68.110.70|172.68.110.70]] 23:40, 1 March 2019 (UTC) | Say I want to build a diverse team or a representative council. And it is more important that the selection is representative of several subpopulations (who should not be voted down by the majority) than that it gives an equal fair chance to anybody. I would cut away the absolute outliers and reduce the weight of the most abundant group - this gives just the area between the two lines. Sebastian --[[Special:Contributions/172.68.110.70|172.68.110.70]] 23:40, 1 March 2019 (UTC) | ||
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Has somebody measured or calculated (by assuming normal distribution) the areas? It seems that the upper area is way smaller than the lower one, but both having the same 'height' in the middle. Is the 52.7% graphically correct? I tried half of the height at 0: .398942 and integrated, then I get 52,6% for the white area and 47,4% for the gray area. On the y-axis it seems that the three visible ticks are .1, .2, .3, then the gray area would be a bit broader than .2 and centered at .1. Sebastian --[[Special:Contributions/172.68.110.70|172.68.110.70]] 23:40, 1 March 2019 (UTC) | Has somebody measured or calculated (by assuming normal distribution) the areas? It seems that the upper area is way smaller than the lower one, but both having the same 'height' in the middle. Is the 52.7% graphically correct? I tried half of the height at 0: .398942 and integrated, then I get 52,6% for the white area and 47,4% for the gray area. On the y-axis it seems that the three visible ticks are .1, .2, .3, then the gray area would be a bit broader than .2 and centered at .1. Sebastian --[[Special:Contributions/172.68.110.70|172.68.110.70]] 23:40, 1 March 2019 (UTC) | ||
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Got [[356:_Nerd_Sniping|Nerd Sniped]] by the number "52.7%", but failed on an analytic solution and settled for a quick and dirty numerical integration instead, which suggested that the exact number might be somewhere between .5268 and .5269, so I think I'm not far from the truth. As I see it, the shaded area is vertically centered around the vertical midpoint, with a relative vertical width chosen such that the shaded area is exactly 50% of the total area under the curve. Just as usual, only with vertical instead of horizontal binning, which of course is the twist that makes this graph puzzling, funny, and completely useless for meaningful interpretation. | Got [[356:_Nerd_Sniping|Nerd Sniped]] by the number "52.7%", but failed on an analytic solution and settled for a quick and dirty numerical integration instead, which suggested that the exact number might be somewhere between .5268 and .5269, so I think I'm not far from the truth. As I see it, the shaded area is vertically centered around the vertical midpoint, with a relative vertical width chosen such that the shaded area is exactly 50% of the total area under the curve. Just as usual, only with vertical instead of horizontal binning, which of course is the twist that makes this graph puzzling, funny, and completely useless for meaningful interpretation. | ||
The label "52.7%" is not an addition to the Midpoint label but instead gives the width of the vertical bin, as a percentage of the vertical height of the curve. I read the tics on the vertical axis to indicate just quarters of the curve maximum, which is consistent with my understanding of "Midpoint". | The label "52.7%" is not an addition to the Midpoint label but instead gives the width of the vertical bin, as a percentage of the vertical height of the curve. I read the tics on the vertical axis to indicate just quarters of the curve maximum, which is consistent with my understanding of "Midpoint". | ||
− | Oh, and you are certainly right in that the marginal distributions at the top and the bottom are asymmetric, as is the gaussian when viewed sideways. | + | Oh, and you are certainly right in that the marginal distributions at the top and the bottom are asymmetric, as is the gaussian when viewed sideways. [[Special:Contributions/172.68.110.64|172.68.110.64]] 23:56, 1 March 2019 (UTC) |
− | [[Special:Contributions/172.68.110.64|172.68.110.64]] 23:56, 1 | ||
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