How to generate random numbers between min and max value with gevrnd?I

I have 16 value with distributed by generalized extreme value. I have k, sigma and mu of this data. I want to increase the data with this distribution between 20 and 21. How can I do it, may I get your help with code sharing?

Thanks

[dpb]

Sorry, I can't understand what you're asking for...can you show example of input and an expected output to describe?

[Adam Danz]

Are you looking for something like

mu = x0 : 20 : x1;

?

[Walter Roberson]

Do I understand properly that currently you have the situation where you have a continuous distribution that includes the range 20 to 21, and that you would like to create a new distribution with increased probability between 20 and 21? If the probability from -inf to 20 is currently p1, and the probability from 20 to 21 is p2, and the probability from 21 to infinity is currently p3, that instead of that [p1, p2, p3] situation, you would like a situation where middle section was C times higher, so your distribution would be in sections with probabilities

[(C*p2 - 1)/(p2 - 1) * p1, C*p2, (C*p2 - 1)/(p2 - 1) * p3]

??

If so then note that the pdf would no longer be continuous and that the sigma and mu would change.

[snr matlb]

Actually, I have a data which is distributed generalized extreme value. The data between 18-20. I have k, sigma and mu of this data. Now, I want to generate random numbers with this k,sigma and mu (with same distribution) but between 20 and 21.

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/stats/prob.normaldistribution.truncate.html

truncate() the distribution. That will automatically re-scale the pdf so that the probability integral over the given range becomes 1.

[snr matlb]

Does it generate numbers between min and max that I determine with generalized extreme value? Will I write generalized extreme value instead of normal? Thanks

[Walter Roberson]

pd = makedist('GeneralizedExtremeValue', k, sigma, mu);
td = truncate(pd, 20, 21);
random(td,1,50)    %will be strictly between 20 and 21

Caution:

Once you truncate the distribution, then the truncated distribution will have a different effective sigma and mu. You cannot just generate values from a distribution and "throw out" values outside the desired range and expect that the result would have the same statistics.

For example I tested with k = 3; sigma = .1; mu = 19; -- notice the mu is outside of the target range 20 to 21. If the generated values restricted to 20 to 21 kept the same mu, then that would imply that mean() of the generated values would have to be 19, but that is obviously impossible when the values are restricted to be between 20 and 21.

[snr matlb]

Wow, As I understand, it is not just possible easily. I am stuck on cloning my real data as regaarding its distribution.

[snr matlb]

I just tried the code, it generated the 50 random numbes however it is not distributed GEV as I check it into Easyfit programme.

[dpb]

"I understand, it is not just possible easily..."

Not only is it not easy, it is theoretically impossible to artifically populate any specific pdf with values in a specific range and not alter the apparent distribution of the resulting sample.

How badly it will be corrupted depends on the distribution and the changes made, but what you've asked for here is pretty drastic departure from what a random sample of the underlying distribution would be...

[dpb]

"The data between 18-20. I have k, sigma and mu of this data. Now, I want to generate random numbers with this k,sigma and mu (with same distribution) but between 20 and 21."

What does that mean, precisely?

You just want to shift the mean and keep the same dispersion or do you think you can bound the distribution between limits?

A GEV distribution is one of a class of EXTREME VALUE distributions...they can be truncated on upper or lower bound depending upon the value of sigma/k + mu, if

• k<0, then p(x)=0, x > -sigma/k+u,
• k>0, then p(x)=0, x < -sigma/k+u.

If k=0, then is unbounded both directions.

You can find a set of parameters that will truncate one side or the other, but simply can't have both truncated.

A set of data such as you describe really doesn't seem likely at all to have come from an extreme value population to begin with...that's just not what would expect to see.

What are these data and where did they come from? What makes you think they should be EV other than you can fit the model to any set of data?

[Walter Roberson]

Your data is between 18 and 20, you said. The mean() and median() of that are going to be below 20: the mean() and median() of a set of data cannot exceed the largest value of the data.

You desire a distribution that gives values between 20 and 21. The mean() and median() of that are going to be above 20: the mean() and median() of a set of data cannot be less than the smallest value of the data.

It is not possible to meet your conditions; you have set up for a contradiction.

[snr matlb]

Now, I have 20 job starting times and instead of looking event time distribution, I checked inter-event dist.It is more likely exponential now. So, I just saved myself from GEV. Now, I will generate new durations to add starting times to get new starting times. Is there any difference between to increase number of jobs in each hour or generate new jobs into a new hour pie. Actually I will have 14 slots for jobs and I will expand the size of my sample to check delays and my model performance to solve it

[Walter Roberson]

Is there any difference between to increase number of jobs in each hour or generate new jobs into a new hour pie.

In some circumstances the difference can be important. As you add more jobs within a deadline, then especially with exponential job times, you might need to go to finer and finer resolution to theoretically fit them -- ending up with situations where milliseconds or nanonseconds are important to meet the deadlines. In practice you probably cannot get millisecond switching, but it would not be uncommon for people to neglect switching time in economic dispatch models.

[snr matlb]

Actually, if I expand hour pies to provide some overcapacities I may get some delay to solve, not miliseconds actually working with minutes. So, I will expand the data but some how with trying to save the distribution as real data to based on real data for further generated. It is better that pure generated numbers I think.

[snr matlb]

Unfortınately, I know I have to make some tune to make them provide some constraints to keep the data tuned with mathematical model constraints.