making normally distributed over Specific Range

how can i make 10 normally distributed number over [8 10] for example

[Torsten]

What so you mean by restricting the normal distribution to a specified interval ?

Use a truncated normal distribution that only has mass on [8 10] ?

Generate random numbers from the usual normal distribution until 10 of them have fallen in the interval [8 10] ?

[mohammad]

It is written in an article that:

10 battery capacities are normally distributed over [22,25] kwh

[Torsten]

Is the article freely available ? Can you give a link ?

[mohammad]

[Torsten]

Use

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

That's the only way I can interprete "normally distributed random numbers over an interval".

[the cyclist]

A google search of terms from that paragraph turned up this thesis.

Perhaps they mention what they mean in another section, or have some code included so that you can see directly. (I didn't look.) Or perhaps you can contact Behnam Khaki and find out.

See my best guess in my answer.

[Torsten]

I agree that most probably, "uniformly" instead of "normally" is meant.

The reason is that it is totally unclear which "universal" normal distribution (mean & variance) could be suited for all the intervals addressed in the thesis.

[John D'Errico]

I would hazard it is unlikely that arrival and departure times would be truly normally distributed in some time interval. Honestly, that would make little sense. However, a uniform distribution of arrivals and departures on some interval makes complete sense.

In turn, that suggests that when that reference talks about normally distributed, they have no idea what they are saying. Sigh.

How about a distribution of battery energies, on an interval? Here, we MIGHT argue for either case. But even then a normal distribution on a fixed, finite interval makes no sense. At best, we might see a truncated normal distribution. So perhaps a charger tries to charge a system to target level, but does not attain that level of charge perfectly due to limits on the ability of the charger to measure what it does, or the capability of the battery to accept a charge. However even there it seems much simpler to argue for a uniform distribution of charge levels over some interval.

Again, I'd give good odds the author had no idea what they meant when they wrote the words normally distributed, not understanding that normally distributed carries with it a very specific connotation in terms of the mathematics. It is not uncommon.

Answer 1

[the cyclist]

It is not possible to have a normal distribution in a finite range.

So, we are all left guessing what the author of this document actually intends.

My best guess is that they actually meant uniformly distributed, rather than normally distributed. Part of the reason I think that is that a normal distribution (even a truncated one), would need to have a variance defined to be fully specified.

If you want to go with that guess, then one way to generate 10 random numbers from a uniform distribution over [8, 10], then

unifrnd(8,10,10,1)

ans = 10×1

8.0782 8.6706 8.9102 9.3289 8.0229 9.8072 9.9151 9.2215 8.0922 8.0361

will do that for you.