This article relies largely or entirely on a
single source. (March 2011) |
Probability density function
c = 1. | |||
Cumulative distribution function
c = 1. | |||
Parameters |
cut-off (
real) curvature ( real) | ||
---|---|---|---|
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[ clarification needed].
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.
The cumulative distribution function (cdf) of the ARGUS distribution is
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.
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.
This article relies largely or entirely on a
single source. (March 2011) |
Probability density function
c = 1. | |||
Cumulative distribution function
c = 1. | |||
Parameters |
cut-off (
real) curvature ( real) | ||
---|---|---|---|
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[ clarification needed].
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.
The cumulative distribution function (cdf) of the ARGUS distribution is
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.
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.