xopto.pf.distribution module¶

class Fractal(alpha: float, range: Tuple[float, float] = (1e-08, 1e-05))[source]¶

Bases: object

Fractal distribution with one parameter alpha:

p(d) = A*(1/d)**alpha

The value of parameter A is computed so as to normalize the integral of the density function on the specified range to 1:

A = (range[0])**(alpha + 1)/(alpha*(1 - (range[0]/range[1])**(alpha + 1)))

Parameters

alpha (float) – Parameter alpha of the fractal distribution.
range (Tuple[float, float]) – The nonzero distribution range as a tuple (start, stop), e.g. use (10e-9, 10e-6) for fractal distribution of particles limited to the finite range from 10 nm to 10 um.

Examples

Creates object representing fractal distribution with alpha=2.4.

>>> fd = Fractal(2.4)
>>> from matplotlib import pyplot as pp
>>> x = np.linspace(10e-9, 10e-6, 1000)
>>> pp.semilogy(x, fd(x))
>>>

property alpha: float¶: Parameter alpha of the fractal distribution (1/d)**alpha.

cdf(x: float) → float[source]¶

property parameters: dict¶: All fractal distribution parameters as a dict object.

property range: Tuple[float, float]¶: Numerical integration range.

raw_moment(n: int) → float[source]¶

Computes the n-th raw moment of the distribution p(x) as:: int(p(x)*x**n) on the interval [range[0], range[1]].

Parameters

n (int) – The requested raw moment.

Returns

n-th raw moment of the distribution defined on the interval
on the interval [range[0], range[1]].

class Mixture(distributions: Tuple[Callable[[float], float]], weights: Tuple[float])[source]¶

Bases: object

Create a mixture distribution instance. Distribution objects must be callable as obj(x) and return the value of distribution at x.

Parameters

distributions (Tuple[Callable[[float], float]]) – Individual distributions of the mixture.
weights (Tuple[float] or np.ndarray) – Weights of the individual distributions. The sum of weights should equal 1.

Examples

Creates object representing normal distribution with mean 1 and standard deviation 0.1.

>>> nd = Normal(1.0, 0.1, clip=5)
>>> from matplotlib import pyplot as pp
>>> x = np.linspace(0.5, 1.5, 1000)
>>> pp.plot(x, nd(x))
>>>

cdf(x: float) → float[source]¶

distribution(index: int) → Callable[[float], float][source]¶

Returns distribution at the specified index or slice.

Parameters: index (int, slice) – Index or slice of the selected distribution.
Returns: pd – The selected distribution object(s).
Return type: Uniform, Normal, Fractal, … or list of Uniform, Normal, Fractal, …

property range: Tuple[float, float]¶: Mixture range.

raw_moment(n: int) → float[source]¶

Computes the n-th raw moment of the distribution p(x) as:: int(p(x)*x**n) on the interval [range[0], range[1]].

Parameters: n (int) – The requested raw moment.
Returns: gn – The n-th raw moment of the distribution defined on the interval on the interval [range[0], range[1]].
Return type: float

weight(index: int) → float[source]¶

Returns weight of the distribution at the specified index or slice.

Parameters: index (int, slice) – Index or slice of the selected distribution weight.
Returns: weight – The selected distribution weight(s).
Return type: float or tuple

class Normal(mean: float, sigma: float, clip: float = 5)[source]¶

Bases: object

Create a Normal distribution instance. The object is callable as obj(x) and returns the value of distribution at x.

Parameters

mean (float) – Normal distribution mean.
sigma (float) – Normal distribution standard deviation.
clip (float) –

The range of Normal distribution is clipped to:
[mean - sigma*clip, mean + sigma*clip]

Examples

Creates object representing normal distribution with mean 1 and standard deviation 0.1.

>>> nd = Normal(1.0, 0.1, clip=5)
>>> from matplotlib import pyplot as pp
>>> x = np.linspace(0.5, 1.5, 1000)
>>> pp.plot(x, nd(x))
>>>

cdf(x: float) → float[source]¶

property mean: float¶: Mean value of the Normal distribution.

property parameters: dict¶: All Normal distribution parameters as a dict object.

property range: Tuple[float, float]¶: Distribution range.

raw_moment(n: int) → float[source]¶

Computes the n-th raw moment of the distribution p(x) as:: int(p(x)*x**n) on the interval [range[0], range[1]].

Parameters

n (int) – The requested raw moment.

Returns

n-th raw moment of the distribution defined on the interval
on the interval [range[0], range[1]].

property sigma: float¶: Standard deviation of the Normal distribution.

class Uniform(lower: float, upper: float)[source]¶

Bases: object

Create a uniform distribution instance. The object is callable as obj(x) and returns the value of distribution at x.

Parameters

lower (float) – Lower bound of the uniform distribution.
upper (float) – Upper bound of the uniform distribution.

Examples

Creates an object representing a uniform distribution on [0, 2].

>>> ud = Uniform(0.0, 2.0)
>>> from matplotlib import pyplot as pp
>>> x = np.linspace(-1.0, 3.0, 1000)
>>> pp.plot(x, ud(x))
>>>

cdf(x: float) → float[source]¶

property lower: float¶: Lower bound of the uniform distribution range.

property parameters: dict¶: All Uniform distribution parameters as a dict object.

property range: Tuple[float, float]¶: The range of uniform distribution as (lower, upper).

raw_moment(n: int) → float[source]¶

Computes the n-th raw moment of the distribution p(x) as:: int(p(x)*x**n) on the interval [range[0], range[1]].

Parameters

n (int) – The requested raw moment.

Returns

n-th raw moment of the distribution defined on the interval
on the interval [range[0], range[1]].

property upper: float¶: Upper bound of the uniform distribution range.