CODEWITHSUNDEEP
algorithmrandomstochastic
Dave
Dave

Reputation: 8090

In what situations does the difference between random numbers generated on [0,1) and those generated on [0,1] make a difference?

I'm used to pseudo random number generators that return floating point values in the half open interval [0,1).

I've seen some reference to RNGs that can return values on the closed interval [0,1], e.g. this implementation of the Mersenne Twister.

I can see reasons why you'd want to exclude one, or both, of the endpoints for mathematical reasons, e.g.

exponentially_distributed=-logf( 1.0-rng() )

always yields a valid number if 0.0<=rng()<1.0.

But I can't think of a case where replacing an rng yielding [0,1] with one that yields [0,1) would produce any practical difference.

In what situations does having a floating point pseudo random number generator that returns values on the closed interval [0,1] absolutely necessary?

Upvotes: 2

Views: 411

Answers (3)

Glenn
Glenn

Reputation: 6563

A compelling reason to use a half-open interval is the use case where you are picking a random array index for some array. When you scale from [0, 1) to integers in [0, arrayLength], it's helpful never to get the value arrayLength, since that is not an index in the array in many language implementations. E.g., Java and ArrayIndexOutOfBoundsException. The half-open interval is a great convenience here.

A reason for having a closed interval [0, 1] is Albin's probability argument. But it's worth noting that mathematically speaking, the probability of picking any particular random number, including 1, in [0, 1], is zero. For pseudo random number generators, though, it will pop up occasionally.

Upvotes: 0

Albin Sunnanbo
Albin Sunnanbo

Reputation: 47048

Can't, figure out when the closed interval would be useful, but the open end interval seems the only reasonable to use way to go.

Lets take coin tossing:

If you say rnd() < 0.5 is head and the rest is tail you will get more tails than heads if you use the closed interval. How many more tails depends on how likely it is to actually get 1.

Upvotes: 1

Alptigin Jalayr
Alptigin Jalayr

Reputation: 709

Maybe if you're randomly generating the probability of an event occurring? If you allow 0, you have to allow 1.

Upvotes: 2

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