Gaussian distribution with randn

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Joseph Lee 2017-11-14

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评论： Joseph Lee 2017-11-14

Is it possible and how can i obtain a Gaussian distribution with randn for

   mean= 0.126 
and it varies by+- 0.02, max=0.146 and min=0.106, 
to generate 1300 random values.

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Rik 2017-11-14

Have you read the documentation (just type doc randn)? You'll need to shift the mean, change the width of the distribution and do something about values outside your range. Think carefully about the order in which you do these.

Joseph Lee 2017-11-14

I tried but generated some negative values instead, which is why i am asking how and whether is it possible or is there a better function to use.

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Answer 1

Akira Agata 2017-11-14

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If you want to generate Gaussian distribution with the given mean and variance (not std), and then extract the values in [min max] range, the following code can do it.

va = 0.02;
mu = 0.126;
ul = 0.146;
ll = 0.106;
x = mu + randn(20000,1)*sqrt(va); % Generate sufficient random numbers
idx = (ll <= x) & (x <= ul); % Extract the value in the given range [min max]
x = x(idx);
x = x(1:1300); % Extract 1300 numbers

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Rik 2017-11-14

在 MATLAB Online 中打开

If your limit values are getting closer to the mean, you will need to progressively generate more values. There will be a function that estimates how many values you will need, but it is probably just easier to hard-code it into the solution given by Akira:

va = 0.02;
mu = 0.126;
ul = 0.146;
ll = 0.106;
nvals=1300;
multiplier=10;%Akira started with 15, for this example, 9 is not always enough, 10 is
x = mu + randn(multiplier*nvals,1)*sqrt(va); % Generate sufficient random numbers
idx = (ll <= x) & (x <= ul); % Extract the value in the given range [min max]
while sum(idx)<nvals
    multiplier=multiplier+1;
    x = mu + randn(multiplier*nvals,1)*sqrt(va); % Generate sufficient random numbers
    idx = (ll <= x) & (x <= ul); % Extract the value in the given range [min max]
end
x = x(idx);
x = x(1:nvals); % Extract 1300 numbers

Joseph Lee 2017-11-14

Thanks for the explanation

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Answer 2

Guillaume 2017-11-14

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编辑：Guillaume 2017-11-14

By definition, a gaussian distribution covers the whole range [-∞, +∞]. If your distribution has a min and max it's not gaussian anymore.

Furthermore, a gaussian distribution is defined by a mean and a standard deviation, not a mean and a range. If a gaussian distribution has a standard deviation of 0.02, you'll still find about 32% of the samples outside of that ±0.02 range.