Probability distribution that always yields the same number

What would be the correct name for a probability distribution which has a 100% chance of yielding a specific number?

I'm tempted to call it "expected value distribution" or some such, but I'm curious to know if there is an actual correct mathematical name or whether it simply is "not a distribution" before I try to come up with something myself. The context is that I am coding a suite of distributions which implement a common interface and there is a requirement that this kind of distribution be available.

• That's typically called a "point mass." So a "point mass at 0" is the probability distribution with $P(\{0\})=1$. – kccu Dec 15 '15 at 23:20
• It's called "degenerate distribution". – A.S. Dec 15 '15 at 23:22
• "Constant" distribution and "deterministic" distribution are also used. – grand_chat Dec 15 '15 at 23:23
• @A.S. : it's a perfectly usual distribution, why degenerate would be a good adjective? Sure, it has no density, but that's the same with Bernoulli distribution or Binomial distribution, so I don't understand – Tryss Dec 15 '15 at 23:32
• @tryss OP is asking about distribution whose support is a single point - which excludes the Binomial. It's called degenerate because randomness (inherent to distributions) degenerates into determinism in this case. I think it's the most appropriate (and most widely used) term as "constant" can be confused with "uniform" and a random variable can be degenerate without being deterministic (if probability of other values is 0, but still a possibility). – A.S. Dec 15 '15 at 23:40

You're probably looking for the Dirac delta distribution. If $x_0$ is the number that will be yielded 100% of the time, you're interested in $\delta(x-x_0)$.