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ARGUS distribution

Probability distribution in physics From Wikipedia, the free encyclopedia

ARGUS distribution
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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[clarification needed].

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Definition

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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.

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Cumulative distribution function

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

.
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Parameter estimation

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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

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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.[2][circular reference]

The variance is:

p = 0.5 gives a regular ARGUS, listed above.

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References

Further reading

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