Moffat distribution
The Moffat distribution, named after the physicist Anthony Moffat, is a continuous probability distribution based upon the Lorentzian distribution. Its particular importance in astrophysics is due to its ability to accurately reconstruct point spread functions, whose wings cannot be accurately portrayed by either a Gaussian or Lorentzian function.
Characterisation
Probability density function
The Moffat distribution can be described in two ways. Firstly as the distribution of a bivariate random variable (X,Y) centred at zero, and secondly as the distribution of the corresponding radii In terms of the random vector (X,Y), the distribution has the probability density function (pdf) where and are seeing dependent parameters. In this form, the distribution is a reparameterisation of a bivariate Student distribution with zero correlation.
In terms of the random variable R, the distribution has density
Relation to other distributions
- Pearson distribution
- Student's t-distribution for
- Normal distribution for , since for the exponential function
References
- A Theoretical Investigation of Focal Stellar Images in the Photographic Emulsion (1969) – A. F. J. Moffat
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univariate
with finite support |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- Multinomial
- Continuous:
- Dirichlet
- Multivariate Laplace
- Multivariate normal
- Multivariate stable
- Multivariate t
- Normal-gamma
- Matrix-valued:
- LKJ
- Matrix normal
- Matrix t
- Matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- Univariate von Mises
- Wrapped normal
- Wrapped Cauchy
- Wrapped exponential
- Wrapped asymmetric Laplace
- Wrapped Lévy
- Bivariate (spherical)
- Kent
- Bivariate (toroidal)
- Bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
- Category
- Commons