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AW: st: Number of values in Gaussian Normal Distribution


From   "Martin Weiss" <martin.weiss1@gmx.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   AW: st: Number of values in Gaussian Normal Distribution
Date   Mon, 5 Oct 2009 15:08:06 +0200

<> 

" With regards to the farthest maximum point that I was getting ,from the
thousands and thousands of draws that I took,that was 6.23026 ,would
that be a lot larger ,to infinitely large,as well ?"


You can explore this question with the simulation below. It will return
5.7297182, so you can view yours as large. You can also increase the number
of repetitions. Still, theoretically any value can be drawn from this
distribution (you may have to wait a couple of million years for it to come
up), so the discussion is indeed a little "fruitless".

*************

//drop it beforehand
capt prog drop sim
set seed 1324543

//define the program
program define sim
    version 10.1
    drop _all
    set obs 10000000
    tempvar z
    gen `z' = rnormal()
    summ `z', mean
end

//simulate it!
simulate max=r(max), /* 
 */ reps(10): sim 

su, mean
di in red  /* 
*/ "Maximum of Maximums: "  /* 
*/ r(max)

*************



HTH
Martin


-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von vmz@vol.net.mt
Gesendet: Montag, 5. Oktober 2009 12:59
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: Number of values in Gaussian Normal Distribution

Thank you for your input.If I understand correctly,if the gap,between two
values in sequence,generated by Stata,were a lot smaller,to infinitely
smaller,I would have gotten ,a lot more than 68518 values ,to an
infinite (uncountable) number of values ,for the points between 0 and
00004.
With regards to the farthest maximum point that I was getting ,from the
thousands and thousands of draws that I took,that was 6.23026 ,would
that be a lot larger ,to infinitely large,as well ?

On 4/10/2009, "David Greenberg" <dg4@nyu.edu> wrote:

>This is a fruitless enterprise. The normal distribution is continuous. It
takes on an infinite number of values even if you restrict yourself to a
part of the distribution that lies between two points. The number of values
is uncountable.
>- David Greenberg, Sociology Department, New York University
>
>----- Original Message -----
>From: "vmz@vol.net.mt" <vmz@vol.net.mt>
>Date: Sunday, October 4, 2009 7:20 pm
>Subject: st: Number of values in Gaussian Normal Distribution
>To: "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
>
>
>> Dear Statlist,
>> I am trying to locate the number of values that constitute a Gaussian
>> Normal Distribution.I am working only on the right side,the positive
>> side,assuming that the left side is the negative of the positive side.
>> The way I am going about concluding the number of values in the right
>> hand side of the Gaussian Normal Distribution,is by taking thousand upon
>> thousands of draws from the Gaussian distribution, and keeping the
>> values for the particular interval,each time accumulating,sorting and
>> dropping the repeating values until I notice that the particular
>> interval doesn't grow any further.
>> I start with the interval (0 to .00004) ,as the first interval and then
>> (.00004 to .00008),as the second interval  ..... ,  ( .0076 to .0078)
>> in
>> the 195th interval ,which seems to have roughly,the same number of
>> values,very close to 68518.I discovered some patterns in the number of
>> values that intervals hold,which made it somewhat easier for me.The
>> following is what I have found so far.Note that the variable x ,is the
>> number of time the same number of values,repeats.t
>>
>> val       min        max       intrv  num  x          tot
>>  68518   0       .00004    .00004  1     0           0
>>  68525 .00776  .0078     .00004  195   195   13362375
>>  50937 .0078   .00784    .00004  196   1     50937
>>  42939 .00784  .00788    .00004  197   0     0
>>  42944 .01556  .0156     .00004  390   194   8331136
>>  34890 .0156   .01564    .00004  391   1     34890
>>  53687 .01564  .01574    .0001   392   0     0
>>  53687 .03114  .03124    .0001   547   156   8375172
>>  13420 .03124  .03128    .00004  548   1     13420
>>  53687 .03128  .03148    .0002   549   0     0
>>  53687 .06228  .06248    .0002   704   156   8375172
>>  18790 .06248  .0626     .00012  705   1     18790
>>  53687 .0626   .063      .0004   706   0     0
>>  53687 .1246   .125      .0004   861   156   8375172
>>  67109 .125    .126      .001    862   0     0
>>  67108 .249    .25       .001    986   125   8388500
>>  33555 .25     .251      .001    987   0     0
>>  33554 .499    .5        .001    1236  250   8388500
>>  33555 .5      .502      .002    1237  0     0
>>  33554 .998    1         .002    1486  250   8388500
>>  33555 1       1.004     .004    1487  0     0
>>  33554 1.996   2         .004    1736  250   8388500
>>  41944 2       2.01      .01     1737  1     41944
>>  41943 2.01    2.02      .01     1738  0     0
>>  41925 3.44    3.45      .01     1881  144   6037200
>>  41927 3.45    3.46      .01     1882  1     41927
>>  41880 3.46    3.47      .01     1883  1     41880
>>  40876 3.47    3.48      .01     1884  1     40876
>>  39480 3.48    3.49      .01     1885  1     39480
>>  38124 3.49    3.5       .01     1886  1     38124
>>  36813 3.5     3.51      .01     1887  1     36813
>>  35541 3.51    3.52      .01     1888  1     35541
>>  34307 3.52    3.53      .01     1889  1     34307
>>  33126 3.53    3.54      .01     1890  1     33126
>>  31980 3.54    3.55      .01     1891  1     31980
>>  30846 3.55    3.56      .01     1892  1     30846
>>  29779 3.56    3.57      .01     1893  1     29779
>>  28723 3.57    3.58      .01     1894  1     28723
>>  27718 3.58    3.59      .01     1895  1     27718
>>  26748 3.59    3.6       .01     1896  1     26748
>>  25797 3.6     3.61      .01     1897  1     25797
>>  24885 3.61    3.62      .01     1898  1     24885
>>  24001 3.62    3.63      .01     1899  1     24001
>>  23140 3.63    3.64      .01     1900  1     23140
>>  22316 3.64    3.65      .01     1901  1     22316
>>  21516 3.65    3.66      .01     1902  1     21516
>>  20743 3.66    3.67      .01     1903  1     20743
>>  19998 3.67    3.68      .01     1904  1     19998
>>  19270 3.68    3.69      .01     1905  1     19270
>>  18569 3.69    3.7       .01     1906  1     18569
>>  17902 3.7     3.71      .01     1907  1     17902
>>  17250 3.71    3.72      .01     1908  1     17250
>>  16623 3.72    3.73      .01     1909  1     16623
>>  15994 3.73    3.74      .01     1910  1     15994
>>  15394 3.74    3.75      .01     1911  1     15394
>>  14826 3.75    3.76      .01     1912  1     14826
>>  14255 3.76    3.77      .01     1913  1     14255
>>  13738 3.77    3.78      .01     1914  1     13738
>>  13235 3.78    3.79      .01     1915  1     13235
>>  12605 3.79    3.78      .01     1916  1     12605
>>  38335 3.78    3.81      .03     1917  1     38335
>>  44761 3.81    3.85      .04     1918  1     44761
>>  47063 3.85    3.9       .05     1919  1     47063
>>  38734 3.9     3.95      .05     1920  1     38734
>>  31780 3.95    4         .05     1921  1     31780
>>  47278 4       4.1       .1      1922  1     47278
>>  52029 4.1     4.3       .2      1923  1     52029
>>  36661 4.3     6.3       2       1924  1     36661
>>
>> According to the previous data,the number of values that make up the
>> Gaussian distribution is 87796774 * 2  = 175593548.I am wondering if
>> there is a simpler way of calculating the number of values,that
>> constitutes the Gaussian Distribution.
>> Vicror M. Zammit
>>
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