# What's the statistical method where you add a certain number to each sample to make the distribution slightly more uniform?

Please forgive my lack of knowledge - it's been a while since I've taken classes in statistics, and even then, it was not my strong point. I'm trying to recall a method used to upweight all values in the distribution using a uniform distribution - it was called something like k+1? Essentially, the method consisted of adding a specific value to all elements in the distribution, to emulate the effect of sampling with a uniform distribution for all elements, so that no element has a value of 0 or close to it.

Edit: I recently (it's currently October 2015) came across the term for this method: it's called adding pseudocounts (or Laplace estimators), at least in the context that I was referring to it. Just adding this in case anyone else can use that information.

• Welcome to Cross Validated!. Please explain what 'normalize' means in this context - unfortunately it has several common meanings. – Scortchi Nov 17 '14 at 22:09
• Can you give some more context, please? Avoiding the ambiguous word 'normalize' would also help (replace it with what that's supposed to actually achieve). Please be explicit about what is actually happening and what kind of task this is for. – Glen_b Nov 17 '14 at 22:11

I believe you're making reference to the effect of a prior distribution over the probability of success $\theta$ on a binomial outcome. For example, if we're thinking about flipping a coin, we might want to place a prior over $\theta=\Pr(\text{heads})$. A beta prior for a binomial likelihood has the benefit of conjugacy, and a $\text{B}(1,1)$ prior is uniform over its support. The result is that each of the "prior heads and tails" is added to the number of heads and tails we actually observed in the experiment: for $k$ heads and $n-k$ tails, the posterior distribution $\theta\sim\text{B}(k+1,n-k+1)$.