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.
The probability density function (pdf) of the ARGUS distribution is:
for . Here and are parameters of the distribution and
where and are the cumulative distribution and probability density functions of the standard normal distribution, respectively.
The cumulative distribution function (cdf) of the ARGUS distribution is
Parameter c is assumed to be known (the kinematic limit of the invariant mass distribution), whereas ÃÂ can be estimated from the sample X<sub>1</sub>, ..., X<sub>n</sub> using the maximum likelihood approach. The estimator is a function of sample second moment, and is given as a solution to the non-linear equation
The solution exists and is unique, provided that the right-hand side is greater than 0.4; the resulting estimator is consistent and asymptotically normal.
Sometimes a more general form is used to describe a more peaking-like distribution:
where ÃÂ(÷) is the gamma function, and ÃÂ(÷,÷) is the upper incomplete gamma function.
Here parameters c, ÃÂ, p represent the cutoff, curvature, and power respectively.
The mode is:
The mean is:
where M(÷,÷,÷) is the Kummer's confluent hypergeometric function.
The variance is:
p = 0.5 gives a regular ARGUS, listed above.