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ARGUS distribution
Probability distribution in physics From Wikipedia, the free encyclopedia
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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].
This article relies largely or entirely on a single source. (March 2011) |
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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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