Have You Seen this Distribution Before?

[Watts]

Any Body Seen This

Has anyone ever seen this before? $P(q) ={\sqrt {\frac{{\pi ^2 }}{{48^2 \cdot \sigma ^2 }}} } \cdot \cosh (2 \cdot \sqrt {\frac{{\pi ^2 }}{{48^2 \cdot \sigma ^2 }}} \cdot (q - \mu ))^{ - 2}$ I managed to derive this distribution(entirly to much time on my hands). It plays by all the rules $P(q)>0 , \int\limits_{ - \infty }^\infty {P(q)dq} = 1 , \int\limits_{ - \infty }^\infty {P(q)\cdot qdq} =\mu , \int\limits_{ - \infty }^\infty {P(q) \cdot (q - \mu )^2 \cdot dq}=\sigma ^2$
.

 

[Valkarie]

Its not listed on Wikipedia so I'm guessing its not an official probability distribution. No, this does not appear to be a formal probability distribution.

 

[tacman]

I have not personally seen this distribution before, but it seems to follow the basic rules and properties of a probability distribution. It is always interesting to come across new distributions and see how they can be applied in different scenarios. Thank you for sharing your findings and derivation with us.