Probability density function No image available |
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Cumulative distribution function No image available |
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Parameters | cut-off (real) χ > 0 curvature (real) |
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Support | |
see text | |
CDF | see text |
Mean | where I1 is the Modified Bessel function of the first kind of order 1, and is given in the text. |
Mode | |
Variance |
In physics, the ARGUS distribution, named after the particle physics experiment ARGUS[1], is the probability distribution of the reconstructed invariant mass of a decayed particle candidate in continuum background.
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The probability density function of the ARGUS distribution is:
for 0 ≤ x < c. Here χ, and c are parameters of the distribution and
and Φ(·), ϕ(·) are the cumulative distribution and probability density functions of the standard normal distribution, respectively.
The cdf of the ARGUS distribution is
Parameter c is assumed to be known (the speed of light), 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.
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.
mode =
p = 0.5 gives a regular ARGUS, listed above.
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