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.Definition
The probability density function 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 of the ARGUS distribution isParameter estimation
Parameter c is assumed to be known, 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.
