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WP section link fix, various tweaks to other WP links
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What the both values of the normal distribution stand for?
What the both values of the normal distribution stand for?


First value μ (mean) and second value σ (standard deviation)?
First value µ (mean) and second value σ (standard deviation)?


[[User:Ssg|Ssg]] 23:13, 5 December 2007 (CET)
[[User:Ssg|Ssg]] 23:13, 5 December 2007 (CET)
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Thanks for your answer.
Thanks for your answer.


I've googled  a (long) bit for that "InverseNormalTable". It seems to be okay. This table is also called "inverse standardized normal distribution" (see http://files.hanser.de/hanser/docs/20040419_24419112747-75_3-446-21594-8Anhang2.pdf)
I've googled  a (long) bit for that "InverseNormalTable". It seems to be okay. This table is also called "inverse standardized normal distribution" (see http://web.archive.org/web/20151010142712/http://files.hanser.de/hanser/docs/20040419_24419112747-75_3-446-21594-8Anhang2.pdf)


The equation for the inverse normal distribution is: x = σ * z + μ
The equation for the inverse normal distribution is: x = σ * z + µ


with:
with:
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:x = result
:x = result
:z = looked up in the z-table (the z-table here is the InverseNormalTable)
:z = looked up in the z-table (the z-table here is the InverseNormalTable)
:μ = mean
:µ = mean
:σ = standard deviation
:σ = standard deviation


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[[User:Neo|Neo]]
[[User:Neo|Neo]]
:The term "inverse normal" is apparently not conventional, and also rather confusing because it can be mistaken as referring to either the [[wikipedia:Normal-inverse_Gaussian_distribution|normal-inverse Gaussian distribution]] or the [[wikipedia:Inverse_Gaussian_distribution|inverse Gaussian distribution]], both of which are rather exotic and irrelevant here.
:The term "inverse normal" is apparently not conventional, and also rather confusing because it can be mistaken as referring to either the [[wp:Normal-inverse Gaussian distribution|normal-inverse Gaussian distribution]] or the [[wp:Inverse Gaussian distribution|inverse Gaussian distribution]], both of which are rather exotic and irrelevant here.
:What we have here is the inverse of the [[wikipedia:Error_function|error function]] or rather that of [[wikipedia:Normal_distribution#Standard_deviation_and_confidence_intervals|erfc(x/sqrt(2))]]. If you have Java installed, [http://onlinestatbook.com/analysis_lab/inverse_normal_dist.html HERE] is a nice applet that you can toy around with to see just what the table in your PDF link corresponds to.
:What we have here is the inverse of the [[wp:Error function|error function]] or rather that of [[wp:Normal distribution#Standard deviation and coverage|erfc(x/sqrt(2))]]. If you have Java installed, [https://onlinestatbook.com/analysis_lab/inverse_normal_dist.html HERE] is a nice applet that you can toy around with to see just what the table in your PDF link corresponds to.
:As further pointed out [[wikipedia:Normal_distribution#Generating_values_for_normal_random_variables|HERE]], inverting the [[wikipedia:Normal_distribution#Cumulative_distribution_function|standard normal cdf]] gives you a way to generate ''normally'' distributed random variables from a ''uniformly'' distributed random variable, which is exactly what Oni does (see Neo's code sample above).
:As further pointed out [[wp:Normal distribution#Generating values from normal distribution|HERE]], inverting the [[wp:Normal distribution#Cumulative distribution function|standard normal cdf]] gives you a way to generate ''normally'' distributed random variables from a ''uniformly'' distributed random variable, which is exactly what Oni does (see Neo's code sample above).
:The float r is a ''uniformly'' distributed random variable in (-1.0,1.0) (@ Neo: please check). Same for x except the interval is now [0.0,10.0). z is a first approximation of erfc(0.0998 * x / sqrt(2)), interpolated linearly between erfc(0.0998 * floorf(x) / sqrt(2)) and erfc(0.0998 * (floorf(x) + 1) / sqrt(2)). The table is thus sampled uniformly.
:The float r is a ''uniformly'' distributed random variable in (-1.0,1.0) (@ Neo: please check). Same for x except the interval is now [0.0,10.0). z is a first approximation of erfc(0.0998 * x / sqrt(2)), interpolated linearly between erfc(0.0998 * floorf(x) / sqrt(2)) and erfc(0.0998 * (floorf(x) + 1) / sqrt(2)). The table is thus sampled uniformly.
:The result ( v1 + z * v2 ) is, to a good approximation, a ''normally'' distributed random variable, centered at v1 and with standard mean deviation v2. Apart from the approximation arising from the linear interpolation, the distribution is cut off at 99.8% of expectancy, so all the values will be within 3.09023*v2 of v1.
:The result ( v1 + z * v2 ) is, to a good approximation, a ''normally'' distributed random variable, centered at v1 and with standard mean deviation v2. Apart from the approximation arising from the linear interpolation, the distribution is cut off at 99.8% of expectancy, so all the values will be within 3.09023*v2 of v1.
::[[User:Geyser|geyser]] 03:12, 7 December 2007 (CET)
::[[User:Geyser|geyser]] 03:12, 7 December 2007 (CET)


Boy, what a ton of interest this little function generates :). The interval for r is [-0.999, 0.999] to be precise (it originates as [-1, 1] and it is multiplied with 0.999). And yes, it is supposed to be distributed uniformly. Here is the (pseudo)random number generator: [[wikipedia:Linear_congruential_generator|linear congruential generator]], the one from Numerical Recipes.
Boy, what a ton of interest this little function generates :). The interval for r is [-0.999, 0.999] to be precise (it originates as [-1, 1] and it is multiplied with 0.999). And yes, it is supposed to be distributed uniformly. Here is the (pseudo)random number generator: [[wp:Linear congruential generator|linear congruential generator]], the one from Numerical Recipes.




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:::That is how I learn particles, too. ^_^ [[User:Gumby|Gumby]] 17:20, 22 May 2009 (UTC)
:::That is how I learn particles, too. ^_^ [[User:Gumby|Gumby]] 17:20, 22 May 2009 (UTC)
{{OBD}}