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Re: st: Number of values in Gaussian Normal Distribution


From   "vmz@vol.net.mt" <vmz@vol.net.mt>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Number of values in Gaussian Normal Distribution
Date   Mon, 05 Oct 2009 11:59:06 +0100

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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