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.

Definition

The probability density function (pdf) of the ARGUS distribution is: for. Here \chi and c are parameters of the distribution and where \Phi(x) and \phi( x ) are the cumulative distribution and probability density functions of the standard normal distribution, respectively.

Cumulative distribution function

The cumulative distribution function (cdf) of the ARGUS distribution is

Parameter estimation

Parameter c is assumed to be known (the kinematic limit of the invariant mass distribution), whereas χ can be estimated from the sample X1, …, Xn 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.

Generalized ARGUS distribution

Sometimes a more general form is used to describe a more peaking-like distribution: where Γ(·) is the gamma function, and Γ(·,·) is the upper incomplete gamma function. Here parameters c, χ, 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.