pyFTS.probabilistic package

Module contents

Probability Distribution objects

Submodules

pyFTS.probabilistic.ProbabilityDistribution module

class pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution(type='KDE', **kwargs)

Bases: object

Represents a discrete or continous probability distribution If type is histogram, the PDF is discrete If type is KDE the PDF is continuous

append(values)

Increment the frequency count for the values

Parameters

values – A list of values to account the frequency

append_interval(intervals)

Increment the frequency count for all values inside an interval

Parameters

intervals – A list of intervals do increment the frequency

averageloglikelihood(data)

Average log likelihood of the probability distribution with respect to data

Parameters

data –

Returns

bins

Number of bins on a discrete PDF

build_cdf_qtl()

crossentropy(q)

Cross entropy between the actual probability distribution and the informed one, H(P,Q) = - ∑ P(x) log ( Q(x) )

Parameters

q – a probabilistic.ProbabilityDistribution object

Returns

Cross entropy between this probability distribution and the given distribution

cumulative(values)

Return the cumulative probability densities for the input values, such that F(x) = P(X <= x)

Parameters

values – A list of input values

Returns

The cumulative probability densities for the input values

density(values)

Return the probability densities for the input values

Parameters

values – List of values to return the densities

Returns

List of probability densities for the input values

differential_offset(value)

Auxiliary function for probability distributions of differentiated data

Parameters

value –

Returns

empiricalloglikelihood()

Empirical Log Likelihood of the probability distribution, L(P) = ∑ log( P(x) )

Returns

entropy()

Return the entropy of the probability distribution, H(P) = E[ -ln P(X) ] = - ∑ P(x) log ( P(x) )

:return:the entropy of the probability distribution

expected_value()

Return the expected value of the distribution, as E[X] = ∑ x * P(x)

Returns

The expected value of the distribution

kullbackleiblerdivergence(q)

Kullback-Leibler divergence between the actual probability distribution and the informed one. DKL(P || Q) = - ∑ P(x) log( P(X) / Q(x) )

Parameters

q – a probabilistic.ProbabilityDistribution object

Returns

Kullback-Leibler divergence

labels

Bins labels on a discrete PDF

plot(axis=None, color='black', tam=[10, 6], title=None)

pseudologlikelihood(data)

Pseudo log likelihood of the probability distribution with respect to data

Parameters

data –

Returns

quantile(values)

Return the Universe of Discourse values in relation to the quantile input values, such that Q(tau) = min( {x | F(x) >= tau })

Parameters

values – input values

Returns

The list of the quantile values for the input values

set(value, density)

Assert a probability ‘density’ for a certain value ‘value’, such that P(value) = density

Parameters

• value – A value in the universe of discourse from the distribution

• density – The probability density to assign to the value

type

If type is histogram, the PDF is discrete If type is KDE the PDF is continuous

uod

Universe of discourse

pyFTS.probabilistic.ProbabilityDistribution.from_point(x, **kwargs)

Create a probability distribution from a scalar value

Parameters

• x – scalar value

• kwargs – common parameters of the distribution

Returns

the ProbabilityDistribution object

pyFTS.probabilistic.kde module

Kernel Density Estimation

class pyFTS.probabilistic.kde.KernelSmoothing(**kwargs)

Bases: object

Kernel Density Estimation

h

Width parameter

kernel

Kernel function

kernel_function(u)

Apply the kernel

Parameters

u –

Returns

probability(x, **kwargs)

Probability of the point x on data

Parameters

• x –

• data –

Returns