Random Number Generation with Parameters (2024)

Hi Demosthenis,

I understand that you want to generate random numbers based on a few rules/parameters.

The first and second conditions can be met using the `randi` function. For instance, you can generate 50% of the total data size (i.e., 500 numbers) within the range of 0-100. The next 20% of the data can be in the range of 101-200, while the remaining numbers can fall within the range of 201-1500. For example, to generate the first 100 numbers in the range of 0-100, you can use:

However, the third condition is unclear and somewhat confusing. It would be helpful if you could provide more details or elaborate further on it.

Hope this helps!

Demosthenis Kasastogiannis 2024 年 8 月 17 日 12:20

I share @John D'Errico's question. I am not sure I understand your reply to his question. My understanding of your wishes is below. If my interpretation is wrong, please explain it again, and explain why you want what you want, because maybe that will help me understand.

My interpretation of your reply to @John D'Errico: You would like consecutive numbers in the "random" data set to differ by 0 to 10%, in 20% of cases. You would like consecutive numbers in the data set to differ by 10-20% in 15% of cases. I think you want consecutive numbers to differ by 50% to 60% in some cases, but I am not sure how often.

In your original post, you said you want

A. Approximately 500 random numbers in the range [0,1500].

B. "50% of numbers between 0 and 100, 25% of numbers between 100 and 200, etc."

C. The requirements about differences between consecutive numbers, described above.

Requirement B is met by an exponential distribution with .

Random numers from this distribution may, rarely, exceed 1500. We can chek for any such values and delete them if found, to comply with requirement A.

The results above indicate that vector y satisfies requirements A and B above.

For requirement C, let us first see what the distribution of percent differences between successive values looks like, if use vector y.

The plot shows that the differece btween consecutive elements is between -1000% and 0%, in approximately 50% of cases, and the difference is between 0 and +1000%, in approximately 45% of cases, and the difference exceeds +1000% in the remaining cases. It makes sense that the difference is negative half the time, for this random sequence. In fact, we know from the definition of percent change, and the fact that the distribution is non-negative, that the successive difference can never be smaller than -100%. Let us make a histogram plot with an expanded horizontal axis to learn more.

The histogram above shows that the difference between successive elements is between -10% and +10% in about 6.0% of cases (the sum of the heights of the two central bars). (Exact values will differ when you run the code, due to randomness.) The difference is in the range -20% to -10%, or +10% to +20%, in 5.4% of cases. I think you want the difference to be between -10% and +10% in 20% of cases, and you want the difference to be in the range -20% to -10%, or +10% to +20%, in 15% of cases.

I have demonstrated how to make a vector of values that satisfies conditions A and B, and I have demonstrated how to evaluate whether condition C is satisfied.

To make a sequence w() that satisfies condition C (but maybe not conditons A and B), you could trythe equation

w(j)=a(j)*w(j-1);

where a(j) is a random number in the range 0.9 to 1.1 in 20% of cases, and a(j) is random in the range (0.8 to 0.9 or 1.1 to 1.2) in 15% of cases, etc. I tried the sequence above. It is tricky to work with. The results are sensitive to the details of the probability distribution of the coefficients a(j). Sequences w(j) that go to 0 (when long) are observed for some a(j) distributions. Some a(j) distributions are likely to produce w(j) sequences that are very large at times.

I would not be surprised if it is impossible to satisfy conditions A, B, and C simultaneously.

Demosthenis Kasastogiannis 約11時間 前

William Rose 約2時間 前