Yashied Posted February 7, 2010 Share Posted February 7, 2010 (edited) I recently had the need to generate random numbers that are distributed according to the law of Gauss. The fact that the function Random() generates a uniformly distributed random numbers. Histogram for the function Random() is as follows (in the range from -1 to 1). By the way, the histogram for RtlRandomEx() function from ntdll.dll is as follows (much worse than for the Random() function - Mersenne Twister). I wrote a function _GRandom() similar to Random(), but returns a numbers that are distributed according to the law of Gauss. I hope that it will be useful for someone. Func _GRandom($Min = 0, $Max = 1, $Variance = Default, $Mean = Default) Local $D, $X1, $X2, $Result If $Min > $Max Then Return SetError(1, 0, 0) EndIf If $Min = $Max Then Return $Min EndIf If $Mean = Default Then $Mean = ($Min + $Max) / 2 EndIf If $Variance = Default Then $Variance = ($Max - $Min) / 2 EndIf If ($Mean < $Min) Or ($Mean > $Max) Then Return SetError(1, 0, 0) EndIf If $Variance <= 0 Then Return SetError(1, 0, 0) EndIf Do Do $X1 = Random(-1, 1) $X2 = Random(-1, 1) $D = $X1 ^ 2 + $X2 ^ 2 Until $D <= 1 $Result = $Mean + $X1 * $Variance * Sqrt(-2 * Log($D) / $D) Until ($Result >= $Min) And (($Result <= $Max)) Return $Result EndFunc ;==>_GRandom$MinThe smallest number to be generated. The default is 0.$MaxThe largest number to be generated. The default is 1.$VarianceVariance relative to the range that specifies by $Min and $Max parameters.$MeanExpected value within the range of $Mim...$Max. The default is the value in the middle of this range - 0.5.Below shows a histogram for this function._GRandom(-1, 1, 0.3, 0)All histograms were drawn by using this function. Edited December 22, 2013 by Yashied My UDFs: iKey | FTP Uploader | Battery Checker | Boot Manager | Font Viewer | UDF Keyword Manager | Run Dialog Replacement | USBProtect | 3D Axis | Calculator | Sleep | iSwitcher | TM | NetHelper | File Types Manager | Control Viewer | SynFolders | DLL Helper Animated Tray Icons UDF Library | Hotkeys UDF Library | Hotkeys Input Control UDF Library | Caret Shape UDF Library | Context Help UDF Library | Most Recently Used List UDF Library | Icons UDF Library | FTP UDF Library | Script Communications UDF Library | Color Chooser UDF Library | Color Picker Control UDF Library | IPHelper (Vista/7) UDF Library | WinAPI Extended UDF Library | WinAPIVhd UDF Library | Icon Chooser UDF Library | Copy UDF Library | Restart UDF Library | Event Log UDF Library | NotifyBox UDF Library | Pop-up Windows UDF Library | TVExplorer UDF Library | GuiHotKey UDF Library | GuiSysLink UDF Library | Package UDF Library | Skin UDF Library | AITray UDF Library | RDC UDF Library Appropriate path | Button text color | Gaussian random numbers | Header's styles (Vista/7) | ICON resource enumeration | Menu & INI | Tabbed string size | Tab's skin | Pop-up circular menu | Progress Bar without animation (Vista/7) | Registry export | Registry path jumping | Unique hardware ID | Windows alignment More... Link to comment Share on other sites More sharing options...

andybiochem Posted February 7, 2010 Share Posted February 7, 2010 (edited) Sorry to be critical, but if you are selectively rejecting numbers based on an upper and lower limit (min,max), then that automatically prevents the distribution from being Gaussian. The true Gaussian integral spans from -∞ to +∞.What you are doing is rejecting everything outside of +/- 2 SD of the mean. Whilst you may end up with a bell-curve of probability favouring the mean (which is probably useful in itself), it isn't Gaussian.The most widely accepted true gaussian algorithms are the Box-Muller method and the Ziggurat Method.[EDIT]Also, what you term 'variance' is actually standard deviation. For example, this:_GRandom(0,200,100,100)should give me a data set with mean = 100 and SD = 10, but it actually gives an SD of 53 ish. Edited February 7, 2010 by andybiochem - Table UDF - create simple data tables - Line Graph UDF GDI+ - quickly create simple line graphs with x and y axes (uses GDI+ with double buffer) - Line Graph UDF - quickly create simple line graphs with x and y axes (uses AI native graphic control) - Barcode Generator Code 128 B C - Create the 1/0 code for barcodes. - WebCam as BarCode Reader - use your webcam to read barcodes - Stereograms!!! - make your own stereograms in AutoIT - Ziggurat Gaussian Distribution RNG - generate random numbers based on normal/gaussian distribution - Box-Muller Gaussian Distribution RNG - generate random numbers based on normal/gaussian distribution - Elastic Radio Buttons - faux-gravity effects in AutoIT (from javascript)- Morse Code Generator - Generate morse code by tapping your spacebar! Link to comment Share on other sites More sharing options...

ValeryVal Posted February 8, 2010 Share Posted February 8, 2010 I wrote a function _GRandom() similar to Random(), but returns a numbers that are distributed according to the law of Gauss. I hope that it will be useful for someone.Your UDF is invalid. See about the true solution here The point of world view Link to comment Share on other sites More sharing options...

Yashied Posted February 8, 2010 Author Share Posted February 8, 2010 (edited) Your UDF is invalid. See about the true solution hereWhat exactly it is invalid? The fact that I limited the range of generated values? Histogram says otherwise.EDIT:Yes, I know that the Gaussian function is defined at -/+ infinity, but in practice, we use a finite interval. Edited February 8, 2010 by Yashied My UDFs: iKey | FTP Uploader | Battery Checker | Boot Manager | Font Viewer | UDF Keyword Manager | Run Dialog Replacement | USBProtect | 3D Axis | Calculator | Sleep | iSwitcher | TM | NetHelper | File Types Manager | Control Viewer | SynFolders | DLL Helper Animated Tray Icons UDF Library | Hotkeys UDF Library | Hotkeys Input Control UDF Library | Caret Shape UDF Library | Context Help UDF Library | Most Recently Used List UDF Library | Icons UDF Library | FTP UDF Library | Script Communications UDF Library | Color Chooser UDF Library | Color Picker Control UDF Library | IPHelper (Vista/7) UDF Library | WinAPI Extended UDF Library | WinAPIVhd UDF Library | Icon Chooser UDF Library | Copy UDF Library | Restart UDF Library | Event Log UDF Library | NotifyBox UDF Library | Pop-up Windows UDF Library | TVExplorer UDF Library | GuiHotKey UDF Library | GuiSysLink UDF Library | Package UDF Library | Skin UDF Library | AITray UDF Library | RDC UDF Library Appropriate path | Button text color | Gaussian random numbers | Header's styles (Vista/7) | ICON resource enumeration | Menu & INI | Tabbed string size | Tab's skin | Pop-up circular menu | Progress Bar without animation (Vista/7) | Registry export | Registry path jumping | Unique hardware ID | Windows alignment More... Link to comment Share on other sites More sharing options...

ValeryVal Posted February 8, 2010 Share Posted February 8, 2010 To verify your UDF's distribution try The Kolmogorov–Smirnov test from any statistical tool.The Kolmogorov–Smirnov test can be modified to serve as a goodness of fit test. In the special case of testing for normality of the distribution, samples are standardized and compared with a standard normal distribution. This is equivalent to setting the mean and variance of the reference distribution equal to the sample estimates, and it is known that using the sample to modify the null hypothesis reduces the power of a test. The point of world view Link to comment Share on other sites More sharing options...

andybiochem Posted February 8, 2010 Share Posted February 8, 2010 Using $s = "" For $i = 1 to 500 $s &= _GRandom(50,150,100,100) & @CRLF Next ClipPut(StringStripWS($s,2)) ...to generate 500 data points with Mean = 100, and SD=10, gives the following analyses... TEST Ho: The sampled population is normally distributed alpha = 0.05 RESULTS n = 500 Mean = 101.7177478 Standard Deviation = 27.56706523 Variance = 759.9430853 K^2 = 6.26 p = 0.04350404 VERDICT Reject Ho: The distribution is not normal. TEST Ho: The sampled population is normally distributed alpha = 0.05 RESULTS n = 500 Mean = 100.1 Standard Deviation = 28.79 Variance = 828.8641 AD = 5.460 P = <0.005 VERDICT Reject Ho: The distribution is not normal. TEST Ho: The sampled population is normally distributed alpha = 0.05 RESULTS n = 500 Mean = 100.1 Standard Deviation = 28.79 Variance = 828.8641 RJ = 0.979 P = <0.010 VERDICT Reject Ho: The distribution is not normal. TEST Ho: The sampled population is normally distributed alpha = 0.05 RESULTS n = 500 Mean = 100.1 Standard Deviation = 28.79 Variance = 828.8641 KS = 0.064 P = <0.010 VERDICT Reject Ho: The distribution is not normal. The only way to get the UDF to pass a test for normality is to set the min and max massively below and above the mean to essentially disable the rejection of the tail-end numbers. I don't want to put you down; it's a good effort...and can be made statistically correct very easily. - Table UDF - create simple data tables - Line Graph UDF GDI+ - quickly create simple line graphs with x and y axes (uses GDI+ with double buffer) - Line Graph UDF - quickly create simple line graphs with x and y axes (uses AI native graphic control) - Barcode Generator Code 128 B C - Create the 1/0 code for barcodes. - WebCam as BarCode Reader - use your webcam to read barcodes - Stereograms!!! - make your own stereograms in AutoIT - Ziggurat Gaussian Distribution RNG - generate random numbers based on normal/gaussian distribution - Box-Muller Gaussian Distribution RNG - generate random numbers based on normal/gaussian distribution - Elastic Radio Buttons - faux-gravity effects in AutoIT (from javascript)- Morse Code Generator - Generate morse code by tapping your spacebar! Link to comment Share on other sites More sharing options...

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