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Re: $rand Bitgod #241771 27/05/13 07:20 PM
Joined: Jul 2006 Posts: 4,149 France W Wims Hoopy frood
Wims Hoopy frood W Joined: Jul 2006 Posts: 4,149 France	It looks like (from irc) you are using the following: Code: timercall 0 5 msg $chan $!gettok(B I N G O G G O O B B B B O N G N B B O I O N G I B I N G O B O, $!rand(1,32), 32) The result you are seeing are correct, what's wrong according to you? Last edited by Wims; 27/05/13 07:26 PM. #mircscripting @ irc.swiftirc.net == the best mIRC help channel

Re: $rand Bitgod #241773 27/05/13 07:41 PM
Joined: Mar 2010 Posts: 57 W Wiz126 Babel fish
Wiz126 Babel fish W Joined: Mar 2010 Posts: 57	$rand() is not broken. You are likely a victim of the clustering illusion. The number of samples you've taken (28 or so) is way too small to make any mathematical claims. That being said, it probably uses C's rand() which is not the best, but it does just fine for most purposes.

Re: $rand

Bitgod #241774 27/05/13 07:51 PM

Joined: Mar 2010

Posts: 57

Wiz126

Babel fish

Wiz126

Babel fish

Joined: Mar 2010

Posts: 57

Seeing the line you were using to generate those results:

Quote:

$!gettok(B I N G O G G O O B B B B O N G N B B O I O N G I B I N G O B O, $!rand(1,32), 32)

Firstly, "biased" is a very ambiguous term, for our purposes I assume you meant that in the context of probability distribution: as in expecting a continuous uniform distribution.

Code:

Given the following string:

B I N G O G G O O B B B B O N G N B B O I O N G I B I N G O B O

We have:

B = 9
I = 4
N = 5
G = 6
O = 8
-------
+ = 32

Expected distribution (given a LARGE ENOUGH sample):

B = 9/32 = 28.125% 
I = 4/32 = 12.5%
N = 5/32 = 15.625%
G = 6/32 = 18.75%
O = 8/32 = 25%

Code:

alias rand_demo {

  ; large enough to make sense of the randomness distribution
  var %x = 1000000

  var %total = %x
  var %b = 0, %i = 0, %n = 0, %g = 0, %o = 0

  while (%x) {
    inc % $+ $exp
    dec %x 
  }

  echo -a B = %b / %total =  $calc(%b / %total * 100)
  echo -a I = %i / %total =  $calc(%i / %total * 100)
  echo -a N = %n / %total =  $calc(%n / %total * 100)
  echo -a G = %g / %total =  $calc(%g / %total * 100)
  echo -a O = %o / %total =  $calc(%o / %total * 100)
}

alias -l exp return $gettok(B I N G O G G O O B B B B O N G N B B O I O N G I B I N G O B O, $rand(1,32), 32)

With 1 million samples, here is my results:

Code:

B = 281972 / 1000000 = 28.1972
I = 125320 / 1000000 = 12.532
N = 156013 / 1000000 = 15.6013
G = 186661 / 1000000 = 18.6661
O = 250034 / 1000000 = 25.0034

Compare to the expected:

Code:

28.1972/28.125 = 100.256711%
12.532/12.5 = 100.256%
15.6013/15.625 = 99.84832%
18.6661/18.75 = 99.552533%
25.0034/25 = 100.0136%

99.55 - 100.25 is perfectly fine. The results are as expected. Of course if you increase the sample even further, you should see the numbers converging at 100%.

Last edited by Wiz126; 27/05/13 08:05 PM.

Re: $rand Bitgod #241775 27/05/13 08:06 PM
Joined: Oct 2003 Posts: 3,918 Montreal, QC, Canada A argv0 Hoopy frood
argv0 Hoopy frood A Joined: Oct 2003 Posts: 3,918 Montreal, QC, Canada	I also don't see any bias: Code: alias testrand { var %buckets = $iif($1,$1,5), %picks = $iif($2,$2,5000) var %i = 1 if ($hget(testrand)) hfree testrand hmake testrand $calc(%buckets * 2) while (%i <= %picks) { hinc testrand n $+ $rand(1,%buckets) inc %i } var %output %i = 1 while (%i <= %buckets) { %output = $addtok(%output, $+(%i,=,$hget(testrand,n $+ %i)), 32) inc %i } echo -a Testing $!rand(1, %buckets $+ ) in %picks samples echo -a Frequencies for $!rand(1, %buckets $+ ) in %picks samples: %output hfree testrand } Running /testrand 5 5000 (default args): Frequencies for $rand(1, 5) in 5000 samples: 1=990 2=1010 3=1000 4=991 5=1009 Running /testrand 100 5000: Frequencies for $rand(1, 100) in 5000 samples: 1=57 2=51 3=55 4=50 5=56 6=54 7=53 8=42 9=50 10=49 11=41 12=49 13=48 14=54 15=42 16=37 17=52 18=37 19=44 20=49 21=38 22=44 23=42 24=47 25=49 26=51 27=57 28=44 29=46 30=45 31=52 32=54 33=60 34=60 35=51 36=39 37=60 38=51 39=51 40=57 41=51 42=49 43=55 44=56 45=49 46=51 47=51 48=55 49=56 50=48 51=58 52=41 53=52 54=44 55=48 56=44 57=42 58=57 59=48 60=62 61=46 62=52 63=52 64=60 65=59 66=56 67=50 68=40 69=41 70=66 71=47 72=50 73=48 74=42 75=48 76=48 77=36 78=46 79=45 80=48 81=52 82=43 83=53 84=54 85=58 86=45 87=57 88=57 89=54 90=54 91=55 92=57 93=43 94=44 95=56 96=46 97=55 98=47 99=55 100=50 I don't see any bias in either of these runs. The first run might look biased to the first bucket, so for good measure I did some more runs: Frequencies for $rand(1, 5) in 10000 samples: 1=2067 2=1966 3=1995 4=2033 5=1939 Frequencies for $rand(1, 5) in 10000 samples: 1=2055 2=2018 3=2008 4=2002 5=1917 Frequencies for $rand(1, 5) in 10000 samples: 1=2031 2=1963 3=1966 4=2000 5=2040 Frequencies for $rand(1, 5) in 10000 samples: 1=2056 2=1988 3=1990 4=2005 5=1961 Frequencies for $rand(1, 5) in 10000 samples: 1=2005 2=2014 3=2000 4=2008 5=1973 Frequencies for $rand(1, 5) in 10000 samples: 1=1997 2=2085 3=2026 4=1960 5=1932 Frequencies for $rand(1, 5) in 10000 samples: 1=1996 2=1945 3=2029 4=1984 5=2046 Frequencies for $rand(1, 5) in 10000 samples: 1=1971 2=1994 3=2020 4=2047 5=1968 Frequencies for $rand(1, 5) in 10000 samples: 1=1977 2=2010 3=2048 4=1922 5=2043 Frequencies for $rand(1, 5) in 10000 samples: 1=2002 2=1927 3=2093 4=1969 5=2009 Frequencies for $rand(1, 5) in 10000 samples: 1=2071 2=1937 3=2010 4=2031 5=1951 Frequencies for $rand(1, 5) in 10000 samples: 1=2054 2=1965 3=2061 4=1949 5=1971 I'm no statistician, but at a quick glance I don't see anything too far out of the ordinary. That said, calculating the relative standard deviation on this is 0.924%, so this data set has a standard deviation of less than %1. That's not what you'd expect to see if the data set was biased. () () Wiz's continuous probability distribution is a much better metric than %RSD-- as I said, I am not a statistician. - argv[0] on EFnet #mIRC - "Life is a pointer to an integer without a cast"

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