Relativistic Breit-Wigner distribution

• rho is the shape parameter.

• scale is (not surprisingly) the scale parameter. This is a true scale parameter, in the sense of https://en.wikipedia.org/wiki/Scale_parameter.

In the wikipedia article https://en.wikipedia.org/wiki/Relativistic_Breit%E2%80%93Wigner_distribution, the parameters are M and Γ. The relations between those parameters and the parameters use here are:

• from (M, Γ) to mpsci’s (rho, scale):

  rho = M/Γ
  scale = Γ
  

• from mpsci’s (rho, scale) to (M, Γ):

  M = rho * scale
  Γ = scale
  

See https://github.com/scipy/scipy/issues/6414 for the details.

mpsci.distributions.rel_breitwigner.cdf(x, rho, scale)

Cumulative distribution function of the relativistic Breit-Wigner distr.

mpsci.distributions.rel_breitwigner.invcdf(p, rho, scale)

Inverse of the CDF of the relativistic Breit-Wigner distribution.

The implementation uses a numerical root finder, so it may be slow, and it may fail to converge for some inputs.

mpsci.distributions.rel_breitwigner.invsf(p, rho, scale)

Inverse of the survival function of the relativistic Breit-Wigner distr.

The implementation uses a numerical root finder, so it may be slow, and it may fail to converge for some inputs.

mpsci.distributions.rel_breitwigner.logpdf(x, rho, scale)

Logarithm of the PDF of the relativistic Breit-Wigner distribution.

mpsci.distributions.rel_breitwigner.mean(rho, scale)

Mean of the relativistic Breit-Wigner distribution.

mpsci.distributions.rel_breitwigner.mode(rho, scale)

Mode of the relativistic Breit-Wigner distribution.

mpsci.distributions.rel_breitwigner.noncentral_moment(n, rho, scale)

n-th noncentral moment of the relativistic Breit-Wigner distribution.

n must be a nonnegative integer. For n > 2, the noncentral moment diverges, so inf is returned.

mpsci.distributions.rel_breitwigner.pdf(x, rho, scale)

Probability density function of the relativistic Breit-Wigner distribution.

mpsci.distributions.rel_breitwigner.sf(x, rho, scale)

Survival function of the relativistic Breit-Wigner distribution.

mpsci.distributions.rel_breitwigner.support(rho, scale)

Support of the relativistic Breit-Wigner distribution.

mpsci.distributions.rel_breitwigner.var(rho, scale)

Variance of the relativistic Breit-Wigner distribution.