Generating samples from Weibull distribution in MATLAB

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I am using the command wblrnd(12.34,1.56) to get 100 different values that lie within the Weibull distribution with those parameters.

But I want those 100 points/values to have the same distribution as the one given by the parameters. Which doesn't happen.

Basically I want, to get 100 values that give me the exact same distribution I had before.

You cannot have the same distribution as the one you're sampling from, unless the number of draws you perform is infinite.

To give you a practical example you can compare how the empirical distribution of your draws, i.e. the histogram, matches the fitted pdf:

subplot(121)
sample = wblrnd(12.34,1.56,100,1);    
histfit(sample,100,'wbl')
title('100 draws')

subplot(122)
sample = wblrnd(12.34,1.56,1e5,1);    
histfit(sample,100,'wbl')
title('100,000 draws')

Also, note that the mean and standard deviations are NOT the arguments of wblrnd(A,B). In other words, mean(sample) is not supposed to converge to 12.34.

You can check on wikipedia: weibull distribution how to retrieve the mean from the shape and scale parameters, i.e. what theoretical mean is given by 12.34 and 1.56.

Weibull Distribution - MATLAB & Simulink, This MATLAB function returns the probability density function (pdf) of the Weibull distribution example. y = wblpdf( x , a ) returns the pdf of the Weibull distribution with scale parameter a Generate C and C++ code using MATLAB® Coder™. According to wblrnd documentation to obtain 100 values that follow a Weibull distribution with parameters 12.34 and 1.56 you should do: wind_velocity = wblrnd(12.34 , 1.56 , 1 , 100); This returns a vector of 1x100 values, from day 1 to 100.

It may be useful for future seekers to use the new Probability Distribution Objects in MATLAB. This highlights utility of makedist(), random(), and pdf() functions (though others work too). See documentation.

You can define the probability distribution object first (shown below with output).

>> pd = makedist('Weibull',12.34,1.56)
pd = 
  WeibullDistribution

  Weibull distribution
    A = 12.34
    B =  1.56

Then obtaining the theoretical mean(), median(), std(), or var() is easy.

>> mean(pd)
ans =
   11.0911
>> var(pd)
ans =
   52.7623
>> median(pd)
ans =
    9.7562

Then generating random variates is simple with the random() command.

n = 2500;    
X = random(pd,n,1);

Note: Probability Distribution Objects introduced in R2013a.

figure, hold on, box on
histogram(X,'Normalization','pdf','DisplayName','Empirical (n = 2500)')
plot([0:.01:50],pdf(pd,[0:.01:50]),'b-','LineWidth',2.5,'DisplayName','Theoretical')  

Reference: Weibull distribution

Weibull probability plot - MATLAB wblplot, You cannot have the same distribution as the one you're sampling from, unless the number of draws you perform is infinite. To give you a  r = wblrnd (a,b,sz1,,szN) generates an array of random numbers from the Weibull distribution, where sz1,,szN indicates the size of each dimension. example. r = wblrnd (a,b,sz) generates an array of random numbers from the Weibull distribution where size vector sz specifies size (r).

Would using rand('seed',0); before your command correct your problem?

Weibull probability density function - MATLAB wblpdf, MATLAB 2017a % Inverse Transform for Weibull distribution % Parameters lambda = 1.5; k = 2; n = 1000; % number of samples to generate  Create a probability distribution object WeibullDistribution by fitting a probability distribution to sample data or by specifying parameter values. Then, use object functions to evaluate the distribution, generate random numbers, and so on.

If instead of obtaining random points you actually want to specify a probability (between zero and one) and get a value from a Weibull distribution with parameters A and B, what you want is the inverse CDF:

X = wblinv(P,A,B)

This is actually what wblrnd is based on (it's a technique called inverse sampling and is commonly used for generating random variates from many distributions). In wblrnd, P = rand(...) effectively. However, if you want to choose probabilities by some other method, wblinv permits you to obtain the values of X that correspond to any P (where P(X) is the probability distribution function, or PDF).

Generating samples from Weibull distribution in MATLAB, In probability theory and statistics, the Weibull distribution /ˈveɪbʊl/ is a continuous probability The moment generating function of the logarithm of a Weibull distributed random samples, then the maximum likelihood estimator for the λ {\displaystyle "Rayleigh Distribution – MATLAB & Simulink – MathWorks Australia". Generate a vector r containing 50 random numbers from the Weibull distribution with the scale parameter 1.2 and the shape parameter 1.5. rng( 'default' ) % For reproducibility r = wblrnd(1.2,1.5,50,1);

According to wblrnd documentation to obtain 100 values that follow a Weibull distribution with parameters 12.34 and 1.56 you should do:

wind_velocity = wblrnd(12.34 , 1.56 , 1 , 100);

This returns a vector of 1x100 values, from day 1 to 100. To obtain the average velocity of those 100 days do:

mean(wind_velocity)

Hope this is what you need.

How to generate a Weibull distribution with inverse transform, MATLAB with functions that compute the pdf, cdf, quantiles, mean and variance (​dispersion) the Weibull Matlab Statistics Toolbox offers functions for the Weibull distribution with two parameters b ax Random numbers generation where x Progressively Type-II Censored Samples, IEEE Transactions on Reliability,. Vol. Generate the Weibull's k and c parameters of those. Plot the probability density function against the wind speed. I am new in Matlab and have not yet been able to do this.

Weibull distribution, to the Weibull distribution, generation of simulated complex multivariate Weibull data number of outlier samples as compared to the Gaussian assumption. Matlab_StatsProject. This is my statistics project under professor Sharmishta Mitra of Indian Institute of Technology Kanpur in 2nd year summers. Problem Statement. Draw random samples of size 10, 30 and 100 from a generalized exponential distribution and fit these to. GE distribution; Weibull distribution

[PDF] addenda to weibull distribution in matlab, Generating Weibull Distributed Random Numbers. This is a step-by-step explaination of how to calculate a transformation function that converts a random variable of one distribution to another distribution. This example uses the Weibull distribution as the intended target distribution. The Weibull distribution is defined as follows,

[PDF] A New Method of Generating Multivariate Weibull , In Shape parameter, enter the shape parameter to define the Weibull distribution. In Scale parameter, enter the scale parameters to define the Weibull distribution. In Threshold parameter, enter the lower bound of the Weibull distribution.

Comments
  • Do you really want to draw Weibull distributed random numbers or do you just want to plot the Weibull pdf that corresponds to these given parameters? If the latter, you should use wblpdf instead.
  • I really need the numbers. wblpdf gives me back the probability of a certain value and not the value itself. To be more specific. This is a daily distribution for mean speeds of wind. And I want to know the mean speed of those 100 days. That is, 1 day had a mean speed of 12 knots 2 days had a mean speed of 8 knots and so on
  • @JoãoSousa, a pdf for a continuous r.v. does not give a probability, rather it is a measure of probability intensity (it is a derivative of a probability). Sorry to nitpick.
  • Re: mean and variance of the Weibull distribution - you can use: [M,V] = wblstat(A,B).
  • What if I create an array with, let's say 100.000 values form the sample = wblrnd(12.34,1.56,1e5,1). Then I run monte carlo simulation where for each iteration 100 points are chosen and a histfit(sample,100,'wbl') is done.Then the goodness of each fit is calculated. And the best goodness is chosen. By the way how can I do the goodness of fit of a histfit?Does anybody know?
  • Following your lead @Olag I did a mini-monte carlo I got to a sample with the same approximate mean, var and weibull parameters as the initial ones [M,V] = wblstat(12.5,1.8); M=roundsd(M,4); V=roundsd(V,4); sample=wblrnd(12.5,1.8,1e5,1); for i=1:5e6 index=randperm(1e5,88); for j=1:size(index,2) s(j)=sample(index(j)); end if M==roundsd(mean(s),4) if V==roundsd(var(s),4) break end end end
  • Thanks but it doesn't
  • Thanks, but that would freeze the way randon numbers are chosen. I have found the solution.