pyFTS.probabilistic package

Module contents

Probability Distribution objects

Submodules

pyFTS.probabilistic.ProbabilityDistribution module

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

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)[source]

Increment the frequency count for the values

Parameters

values – A list of values to account the frequency

append_interval(intervals)[source]

Increment the frequency count for all values inside an interval

Parameters

intervals – A list of intervals do increment the frequency

averageloglikelihood(data)[source]

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()[source]
crossentropy(q)[source]

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)[source]

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)[source]

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)[source]

Auxiliary function for probability distributions of differentiated data

Parameters

value –

Returns

empiricalloglikelihood()[source]

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

Returns

entropy()[source]

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()[source]

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

Returns

The expected value of the distribution

kullbackleiblerdivergence(q)[source]

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)[source]
pseudologlikelihood(data)[source]

Pseudo log likelihood of the probability distribution with respect to data

Parameters

data –

Returns

quantile(values)[source]

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)[source]

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)[source]

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)[source]

Bases: object

Kernel Density Estimation

h

Width parameter

kernel

Kernel function

kernel_function(u)[source]

Apply the kernel

Parameters

u –

Returns

probability(x, **kwargs)[source]

Probability of the point x on data

Parameters

  • x –

  • data –

Returns