Unifrnd generates a large number of uniform distributions. Is a part of it still uniform？

Excuse me, I use a = unifrnd (0.2,0.550000,1); generate these 50000 random numbers that conform to (0.2,0.5) uniform distribution, and then I take 3000, for example, am = a (1:3000,:). Are these 3000 random numbers also conform to (0.2,0.5) uniform distribution? thank you!

Answer 1

[John D'Errico]

Short answer: Yes.

Long answer: yyyyyeeeeeessssssss.

Think of it like this: These numbers have the property of beeing iid. Independent, identically distributed. And that tells you if you take some subset of them that is not based on their value, they will still have the same distribution.

Yes, if you consider a subset where you choose only those that are less than 0.3, then they will not have the same overall distribution. But a subset chosen arbitrarily based only on index will still have the original distribution.

[yuxiao qi]

'if you consider a subset where you choose only those that are less than 0.3, then they will not have the same overall distribution.' so why you say this, i don't understand,why this subset will not have the same overall distribution? thank you

[Steven Lord]

Generate some random numbers

x = rand(1, 1e5);
bins = 0:0.125:1;

Create three histogram objects.The first has the data binned with bins of width 0.125.

histogram(x, bins)

The second has the data from the first 1e4 elements in x binned with bins of width 0.125.

histogram(x(1:1e4), bins)

The third has data from those elements of x that are greater than 0.25 binned with bins of width 0.125.

histogram(x(x > 0.25), bins)

The first two histograms look very similar, just the scaling on the Y axis is different. The third histogram doesn't look like the other two, because the first two bins are completely empty.

[yuxiao qi]

Thank you very much. I see what you say. I want to ask a little more, so by unifrnd(0.2,0.5,6000,1) we generate 6000 random numbers, and I want to estimate how many of these values are greater than or equal to 0.3, can we estimate them by the formula 6000*(0.5-0.3)/(0.5-0.2)?

[Steven Lord]

Do you want to estimate how many there should be theoretically or do you want to count how many there are practically?

[yuxiao qi]

just theoretical estimate

[John D'Errico]

"i don't understand,why this subset will not have the same overall distribution? thank you"

This is getting off-topic, based on an offhand comment I made. Sigh. If I start with a set of points, all of which are assumed to lie in the interval [0.2,0.5], and are uniformly distributed on that interval. The the population mean of that set must be 0.35. Do you agree with that?

Now I extract only the subset that lies in the sub-interval [0.2,0.3]. Can the mean of this subset possibly be larger than 0.3?

The subset chosen will be UNIFORMLY distributed still. But the distribution will not possibly be the same as the original set, since the mean is different.

Yes, you can estimate the relative fraction of that set that lies less than 0.3, using the formula you show. That will not be the exact fraction in general, because this is a randomly generated set.

[yuxiao qi]

thank you