S.Mustonen (2003)

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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