@MikeL. Thats what Im talking about. I meant that srinking / expanding, moving horizontally feels wrong. I'm thinking that only vertical modifications leave the original behaviour intact (as we are working with probabilities)

@Oxy well, moving it horizontally changes your domain. That may or may not be what you want to do.

I think it's not. Wihtout any actual restriction, if I need the lowes point to end up beeing 0 and the hightest 1, moving the domain just for that feels the less appropriate way to do it.

@MikeL. Anyway, I modified it to only change the vertical behavour. It does not matter much how do I 'stomp' it vertically or move it in the same direction, it's still has got the same proportional behaviour. Changing the domain does not feel right to 'just' fit it to 0..1

@MikeL. Humm... In your algorithm you used the same random value to chose CDF , then modified it to use on the CDF itself

@Oxy yep

It's less correct, from a randomness standpoint, to use it this way even knowing that each operation a computer performs on a floating point number makes it less exact, or to use another fresh random (provided taht computers don't give true randomness) to prevent modification?

It shouldn't make a difference... but if the operations on floats have tendency to de modified in some way, and not in both ways, it could make the random distribution less 'continuous', wouldn't it? (ie, always truncating, or something like tending to lose a bit or two at the end.)

@MikeL. I know computers are bad at handling both decimals and randomness... so the question is more about, what's worse? Using more pseudo-random numbers or making the cpu woble more the same decimals? From a coding standpoint, both are equally easy, and the difference in efficiency is negligible.

So, as it's equally easy for me, I'd like to know what is more correct

@Oxy The answer is that it depends. If you have a physical source of entropy, it's better to draw another random sample, but with most practical PRNGs you probably want to go the way of scaling.

Yes, you lose some precision, but that's not that big of a deal and doing it the other way you're cutting your RNG period in half.

Nice! That was the kind of tradeoff I'm willing to make. Let's let the RNG live longer, then. If I ever need more precisions, it's as easy as to change from doubles to long doubles :D (It's not... but well, something could be done, probably easier than coming up with a RNG with a period orders of magnitude greater, that's for sure)

@HDE226868 I'm entering the second phase of the answer. Looks quite simple. But I have a question. Since from mass we approximate the luminosity, and later is said than for main sequence star's mass and luminosity we can know the time it has been in main sequence.... Wouldn't that make our stars always the same main sequence age (for the same masses and luminosities)?

I'm asking this because all that is given (REALLY useful and meaty stuff) concerns main sequences

And maybe, as we already have the mass of the star, we could make up an age and THEN see if it's main sequence, still in formation, or already dead. Sounds stupid? Maybe there exists some already studied solution to this but is too complex... well, any approximation would be better than have an universe which is only main sequence stars.

@Oxy Well, yes, but those are only approximations. Various factors, ranging from metallicity to rotation to pulsations to I-don't-know-what, can impact the parameters of a star, and lead to subtle differences in its structure and evolution, which then play a larger role in its development.