random numbers

[Ray Andrews <rayandrews@xxxxxxxxxxx>]

    I was exploring Benford's Law thusly: (not
      very elegant but it works):
      
      #!/bin/zsh
      
      integer level=    
      integer a1=0
      integer a2=0
      integer a3=0
      integer a4=0
      integer a5=0
      integer a6=0
      integer a7=0
      integer a8=0
      integer a9=0
      
      for ((level=1; level<=1000; level++)); do
      
      #First tests:
      var=$RANDOM
      
      #Second tests:
      #var=$(shuf -i 1-1000 -n 1)
      
          if [ ${var[1]} = '1' ]; then ((a1++)); fi
          if [ ${var[1]} = '2' ]; then ((a2++)); fi
          if [ ${var[1]} = '3' ]; then ((a3++)); fi
          if [ ${var[1]} = '4' ]; then ((a4++)); fi
          if [ ${var[1]} = '5' ]; then ((a5++)); fi
          if [ ${var[1]} = '6' ]; then ((a6++)); fi
          if [ ${var[1]} = '7' ]; then ((a7++)); fi
          if [ ${var[1]} = '8' ]; then ((a8++)); fi
          if [ ${var[1]} = '9' ]; then ((a9++)); fi
      done
      
      echo a1 is: $a1
      echo a2 is: $a2
      echo a3 is: $a3
      echo a4 is: $a4
      echo a5 is: $a5
      echo a6 is: $a6
      echo a7 is: $a7
      echo a8 is: $a8
      echo a9 is: $a9
      
---------------------------------------------------------------------------------
      
      First tests give close to this:
      
      5 /aWorking/Zsh/Source/Wk/Boneyard/Math 1 % . ./test1
      a1 is: 339
      a2 is: 336
      a3 is: 134
      a4 is: 27
      a5 is: 31
      a6 is: 25
      a7 is: 28
      a8 is: 40
      a9 is: 40
      
      Second tests close to this:
      
      5 /aWorking/Zsh/Source/Wk/Boneyard/Math 1 % . ./test1
      a1 is: 110
      a2 is: 102
      a3 is: 114
      a4 is: 114
      a5 is: 107
      a6 is: 99
      a7 is: 135
      a8 is: 108
      a9 is: 111
      
---------------------------------------------------------------------------------------------------
      
      I think i know why, it's because zsh's RANDOM tops out at 32,767,
      but this insures that the first digit of a string of random
      numbers isn't random but strongly weighted to 1 and 2, with 3 also
      weighted.  Is this worth worrying about?  I'd say so.  Perhaps it
      should max out at 10,000 or 100,000 or even offer a user
      selectable range?  Or do we have other tricks for coping with
      this?  I find zsh to be quite competent mathematically so having
      to use an external utility to get really random numbers seems not
      up to snuff.