Random number generate in an interval

Hi community,

I would like to generate random number in the follow distribuition: Normal, Gamma and Weibull.

Amount of data required: 5000 numbers at interval [a,b]

At the example, it was used the follow code:

A = linspace(0,1,5000)
sr = size(A)
b = normrnd(27.5,15.73,sr)
plot(b)

Its works, however, the valid interval to generate was [1,54]

Can us help me, please?

Yours faithfully

[William Rose]

@Guilherme Lopes de Campos,

[edit: fix spelling errors]

It is not possible to generate random numbers that follow the normal or Weibull or gamma distributions, and limit them to a finite range, because all of those distributions have non-zero probability out to infinity. The latter two go from 0 to +Inf, and the normal from -Inf to +Inf.

If you specify a mean and s.d. for normal, or a shape and a scale for the Weibull and gamma, you can generate random numbers, and then you can clip any values outside your interval of interest. Technically, once you have done this, the remaining numbers do not have the originally specified distribution. In practice, the clipping won't make a difference, if the probability of extreme values was extremely small anyway, compared to the sample size.

I hope this helps.

[Walter Roberson]

(27.5 - 1) / 15.73

ans = 1.6847

(54 - 27.5) / 15.73

ans = 1.6847

Less than 2 standard distributions -- the excluded area is non-trivial, and will make a significant difference in normality.

A = linspace(0,1,5000)

A = 1×5000

0 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036 0.0038 0.0040 0.0042 0.0044 0.0046 0.0048 0.0050 0.0052 0.0054 0.0056 0.0058

sr = size(A)

sr = 1×2

1 5000

b = normrnd(27.5,15.73,sr);

[min(b), max(b)]

ans = 1×2

-45.4716 84.9146

pd = fitdist(b.','Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 27.3657   [26.9338, 27.7975]
    sigma = 15.5758   [15.2764, 15.8872]

btrunc = max(1, min(b, 54));
[min(btrunc), max(btrunc)]

ans = 1×2

1 54

pd2 = fitdist(btrunc .', 'Normal')

pd2 = 
  NormalDistribution

  Normal distribution
       mu =  27.383   [26.9857, 27.7802]
    sigma = 14.3283   [14.0529, 14.6148]

The standard distribution of the truncated version is notably different.

[William Rose]

@Guilherme Lopes de Campos,

@Walter Roberson is exactly right that if and , then clipping to [1,54] leaves a distinctly non-normal distribution. I was not sure from your orignal post if the code

b = normrnd(27.5,15.73,sr)

was just a separate example, or if it represented the mean and SD which you actually want. You will need to calculate a bit to translate a desired mean and SD to shape and scale parameters for gamma (easy) or Weibull (less easy).

[Bruno Luong]

Careful

b = normrnd(27.5,15.73,sr);
btrunc = max(1, min(b, 54));

This clipping does NOT generate truncated normal distribution which is conditional probability (rejection) and NOT clipping probability

[Paul]

To illustrate @Bruno Luong's point

rng(100)
pd = truncate(makedist('Normal',27.5,15.73),1,54);
x = 1:.01:54;
figure
plot(x,pdf(pd,x))
hold on
b = normrnd(27.5,15.73,[1 500000]);
btrunc = max(1, min(b, 54));
histogram(btrunc,'Normalization','pdf')

figure
plot(x,pdf(pd,x),'LineWidth',5)
hold on
breject = b(b>=1 & b<=54);
histogram(breject,'Normalization','pdf')

[Walter Roberson]

Right, different interpretations of what "clipping" means in the context.

format long g
b = normrnd(27.5,15.73,[1 500000]);
out_of_range = (b < 1) | (b > 54);
mean(out_of_range) * 100

ans = 
                     9.195

so over 9% of the samples are outside of the target range

[Walter Roberson]

@Guilherme Lopes de Campos comments to @Bruno Luong

It works! Thank you very much

Answer 1

[the cyclist]

A normal distribution, by definition, has support from negative infinity to positive infinity. You cannot have both a normal distribution and a finite range.

You can use the truncate function to create a truncated normal distribution object, and draw values from that. (See the second example on that page.) Is that what you want?

Answer 2

[Bruno Luong]

The file TruncatedGaussian.m is from this page https://www.mathworks.com/matlabcentral/fileexchange/23832-truncated-gaussian?s_tid=srchtitle

This doesn't need stat toolbox.

sigma = 15.73;
mu = 27.5;
interval = [1 54];
n = [1, 5000000];
X = TruncatedGaussian(-sigma,interval-mu,n) + mu;
histogram(X)