Environment for creative processing of text and numerical data

Central limit theorem

S.Mustonen (2003)

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   1 *
   2 *Central limit theorem
   3 *
   4 *Sucro SUMDISTR shows how the sum of independent random variables
   5 *tends to the normal distribution when the number of variables grows.
   6 *SUMDISTR works in the special case where the variables have the same
   7 *discrete distribution given by the user.
   8 *SUMDISTR displays density functions of sums on the screen automatically
   9 *step by step and compares them to the normal distribution.
  10 *It also computes a deviation from the normal distribution according to
  11 *the Kolmogorov-Smirnov test statistics.
  12 *
  13 *Here only a collection of pictures is shown by letting the sucro
  14 *save the partial graphs in a PostScript file.
  15 *
  16 *The sum distribution may have very interesting transient forms
  17 *depending on the basic distribution before the ultimate 'normalization'.
  18 *In this example we have a discrete uniform distribution with values
  19 *0,1,2,...,19, but the probability of 19 is ten-fold when compared to
  20 *others. Thus there is a peak on the right side of the distribution.
  21 *
  22 *It is sufficient to give values proportional to actual probabilities.
  23 *MAT Q1=CON(20,1)               / Definition of probabilities as a vector
  24 *MAT Q1(20,1)=10                / Setting the peak
  25 */SUMDISTR Q1  / NMAX=9 PS=SUM  / Running the demo and saving the graphs
  26 *
  27 *Overlaying density function of normal distribution (SUM0, also plotted
  28 *by SUMDISTR) and the densities of sums:
  29 *EPS JOIN S1,SUM0,SUM1 
  30 *EPS JOIN S2,SUM0,SUM2 
  31 *EPS JOIN S3,SUM0,SUM3 
  32 *EPS JOIN S4,SUM0,SUM4 
  33 *EPS JOIN S5,SUM0,SUM5 
  34 *EPS JOIN S6,SUM0,SUM6 
  35 *EPS JOIN S7,SUM0,SUM7 
  36 *EPS JOIN S8,SUM0,SUM8 
  37 *EPS JOIN S9,SUM0,SUM9 
  38 *
  39 *Combining the partial graphs and setting a 3 x 3 array of pictures
  40 *as a PostScript file ALL.PS:
  41 *EPS JOIN ALL,A1,A2,A3,A4,A5,A6,A7,A8,A9 
  42 *A1=S1,0000,1100,0.333,0.333
  43 *A2=S2,0550,1100,0.333,0.333
  44 *A3=S3,1100,1100,0.333,0.333
  45 *A4=S4,0000,0550,0.333,0.333
  46 *A5=S5,0550,0550,0.333,0.333
  47 *A6=S6,1100,0550,0.333,0.333
  48 *A7=S7,0000,0000,0.333,0.333
  49 *A8=S8,0550,0000,0.333,0.333
  50 *A9=S9,1100,0000,0.333,0.333
  51 *A9=S9,1100,0000,0.333,0.333
  52 *

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