Dear Researchers,
I hope this question finds you well.
To generate random numbers from a given probability distribution using Arena, just use Arena Input Analyzer>>File>>Data file>>Generate New>>Window>>Input Data.
But when I want to generate random numbers from the following distribution, I can not know the values of Min= , Max= , and the number which multiplied to the Beta distribution.
The distribution is "0.03+1.97*BETA(0.79,0.577)"
I know that random numbers can be generated from a given distribution using programes beside Arena such as R, Matlab, Excel,....
Any answer is appreciated.
Regards,
Mahmoud
Dear Eng. Mahmoud,
I hope you are doing well.
I searched for Beta distribution for a little time. I hope that this answer will help with your question. I have read that beta dist. function f(x) have x values between 0 and 1.
A beta random variable, X, assumes values in the unit interval S = [ 0, 1], although it may be scaled and shifted to any interval.
For example, the following distribution 10 + 20 (Beta(0.988, 1.02)) has its state space-range of x values to be in the range [10, 30] rather than the standard state space S = [0, 1]. Thus, the beta distribution was transformed from the interval [0, 1] to the interval [10, 30] by a linear transformation in the expression above.
So, I think that Min and Max values should be 0.03 and 2.0.
Note that the beta distribution in Arena has the parameters in reverse order (Fig. 1). So, alpha and beta values should be reversed in the text boxes.
[Please, read pages 46, 132 in the book which its link is attached)
Last point that I want to discuss is that you could write an expression to set the distribution as needed, as our case. For example, when using a process module and want to determine the delay type for this process using and want to determine a special expression. You can click right in the expression text box and choose Build Expression and write your expression for generating values to your distribution by writing
"0.03 + 1.97 * Beta ( 0.79,0.577 )" (attached Fig. 2 and 3).
I want to recommend attached book titled "Simulation Modeling and Analysis with Arena" by Tayfur Altiok and Benjamin Melamed. I think its language it very excellent and simple. Also, I have learned a lot from its well explained and formed examples.
There is another link for YouTube video explaining beta distribution. I hope that helps inshallah.
I hope that I understand the question well and hope that the discussion are helpful and not have distracted you. Please tell me if there is a misunderstanding of the question. I'm looking forward to more discussion.
Best Regards,
Emad
http://bookzz.org/book/693221/6d86e8
https://www.youtube.com/watch?v=G_UFHE93uXs
Dear Eng Emad,
Thank you very much for the detailed answer. I really appreciate your effort.
Regarding the BETA distribution parameters, their name in the the random numbers generation window is Alpha1 and Alpha2 not Beta and Alpha (Attached). So, I think there is no need to reverse the parameters' values. Therefore, for my distribution Alpha1=0.79 and Alpha2=0.577, are not they?
Best Regards,
Mahmoud
Dear Eng. Mahmoud,
I think your explanation might be true as the parameters names tell.
But I read this note in the book "Note that the beta distribution in Arena has the parameters in reverse order" in page 46. Also- from figure 1 (Table 7.2 in book)- we see that the order of parameters are beta followed by alpha.
I think that alpha 1 here is just referring to the first parameter that is used in beta distribution in arena. Because Arena considers the first parameter as beta, I think that we should add beta value to the first text box. And supply the second text box with the value of alpha.
- Badges
- Science topic