Distributions

class maoud.distributions.AlphaMu(alpha, mu)[source]

Defines the α — μ probability distribution. For the theorectical aspects of the α — μ distribution, see M. D. Yacoub, The α — μ distribution: A physical fading model for the Stacy distribution, IEEE Trans. Veh. Technol., vol. 56, no. 1, pp. 27–34, 2007.

Attributes

alpha, mu (float, float) Parameters that define the α — μ distribution.

Methods

pdf(x) Defines a univariate α — μ probability density function.
rvs(x, size) Returns a sample of length size in the range [x.min(), x.max()].
pdf(x)[source]

Defines a univariate α — μ probability density function.

Parameters:

x : 1darray

Points where to evaluate the pdf.
Returns:

pdf : 1darray

pdf values at x.
class maoud.distributions.ComplexAlphaMu(alpha, mu)[source]

Methods

envelope_pdf(x)
pdf(x)
rvs(x, y, size) Returns a sample of length size in the range [x.min(), x.max()] and [y.min(), y.max()] for the real and imaginary parts.
envelope_pdf(x)[source]
pdf(x)[source]
class maoud.distributions.ComplexDistribution[source]

Defines a class for probability distribution arising from a complex random variable Z = X + jY, where j = sqrt(-1).

Methods

envelope_pdf(x)
pdf(x) Defines a 1D probability density function.
rvs(x, y, size) Returns a sample of length size in the range [x.min(), x.max()] and [y.min(), y.max()] for the real and imaginary parts.
envelope_pdf(x)[source]
rvs(x, y, size)[source]

Returns a sample of length size in the range [x.min(), x.max()] and [y.min(), y.max()] for the real and imaginary parts.

Parameters:

x, y : arrays

The support of the pdf of the real and imaginary parts, respectively.

size : int

Size of the sample (number of realizations).
class maoud.distributions.ComplexEtaMu(eta, mu)[source]

Methods

envelope_pdf(x)
pdf(x)
rvs(x, y, size) Returns a sample of length size in the range [x.min(), x.max()] and [y.min(), y.max()] for the real and imaginary parts.
pdf(x)[source]
class maoud.distributions.ComplexKappaMu(kappa, mu, phi)[source]

Methods

imag_part(x)
real_part(x)
rvs(x, y, size)
imag_part(x)[source]
real_part(x)[source]
rvs(x, y, size)[source]
class maoud.distributions.Distribution[source]

An abstract class for a probability distribution.

Methods

pdf(x) Defines a 1D probability density function.
rvs(x, size) Returns a sample of length size in the range [x.min(), x.max()].
pdf(x)[source]

Defines a 1D probability density function.

Parameters:

x : 1darray

Points where to evaluate the pdf.
Returns:

pdf : 1darray

pdf values at x.
rvs(x, size)[source]

Returns a sample of length size in the range [x.min(), x.max()].

Parameters:

x : array

The support of the pdf.

size : int

Size of the sample (number of realizations).
class maoud.distributions.EtaMu(eta, mu)[source]

Defines the eta — μ probability distribution. For the theorectical aspects of the eta — μ distribution, see [ADD REFERENCE]

Attributes

eta, mu (float, float) Parameters that define the eta — μ distribution.

Methods

pdf(x)
rvs(x, size) Returns a sample of length size in the range [x.min(), x.max()].
pdf(x)[source]
class maoud.distributions.KappaMu(kappa, mu)[source]

Defines the kappa — μ probability distribution. For the theorectical aspects of the kappa — μ distribution, see [ADD REFERENCE]

Attributes

kappa, mu (float, float) Parameters that define the kappa — μ distribution.

Methods

pdf(x)
rvs(x, size) Returns a sample of length size in the range [x.min(), x.max()].
pdf(x)[source]