ARGUS distribution

 I_1(\tfrac{\chi^2}{4})}{ \Psi(\chi) }</math><br><br> where "I"1 is the Modified Bessel function of the first kind of order 1, and formula_1 is given in the text.
 | median =
 | mode = formula_2
 | variance = formula_3
 | skewness =
 | kurtosis =
 | entropy =
 | mgf =
 | char =
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 formula_5. Here formula_6 and formula_7 are parameters of the distribution and
where formula_9 and formula_10 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 "X"1, …, "X""n" 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 formula_13 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.