ARGUS distribution

In physics, the ARGUS distribution, named after the particle physics experiment ARGUS, is the probability distribution of the reconstructed invariant mass of a decayed particle candidate in continuum background.

ARGUS

Probability density function c = 1.
Cumulative distribution function c = 1.
Parameters	${\displaystyle c>0}$ cut-off (real) ${\displaystyle \chi >0}$ curvature (real)
Support	${\displaystyle x\in (0,c)\!}$
PDF	see text
CDF	see text
Mean	${\displaystyle \mu =c{\sqrt {\pi /8}}\;{\frac {\chi e^{-{\frac {\chi ^{2}}{4}}}I_{1}({\tfrac {\chi ^{2}}{4}})}{\Psi (\chi )}}}$ where I1 is the Modified Bessel function of the first kind of order 1, and ${\displaystyle \Psi (x)}$ is given in the text.
Mode	${\displaystyle {\frac {c}{{\sqrt {2}}\chi }}{\sqrt {(\chi ^{2}-2)+{\sqrt {\chi ^{4}+4}}}}}$
Variance	${\displaystyle c^{2}\!\left(1-{\frac {3}{\chi ^{2}}}+{\frac {\chi \phi (\chi )}{\Psi (\chi )}}\right)-\mu ^{2}}$