# Probability transformed around mean - does this already exist?

Non-trained in mathematics here so bear with me.

I'm using a formula that takes a Gaussian distribution and sets $F(x)$ where $x$ is equal to the mean to be $1.0$ and to either side drops off symmetrically. I am using it to test how well an observation x fits in the center of a distribution. I am certain this exists and I would prefer to know what it is called.

$\overline{x} = \mu - \left| \mu - x_{n} \right|$ for a given nth x.

So $F\left(\overline{x}\right)$ maximizes at $\mu$.

Again, pardon my ignorance, but my searching failed to turn up what this is called. Thanks!

Illustration: [1]

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Dont follow after the words 'and sets F(x)...' –  Lost1 Jan 13 at 22:20
my first idea would be the normal distribution but then what do you mean by "to either side drops off proportionally", maybe you mean a triangle distribution –  Willemien Jan 13 at 22:24
Instead of "proportionally," do you mean "symmetrically?" –  John Jan 13 at 22:27
@John I guess you know this but this is for the OP as well, just saying the distribution is symetrical is not enough to decide what kind of distribution it is, the OP needs to describe the distribution in much more detail, I was wondering if I should flag the question –  Willemien Jan 15 at 12:49
@Willemien yes, absolutely. Just trying to help clarify the question in some way. –  John Jan 15 at 18:09