PINE LIBRARY

Probability

Updated

Library "Probability"

erf(value) Complementary error function
Parameters:

value: float, value to test.

Returns: float

ierf_mcgiles(value) Computes the inverse error function using the Mc Giles method, sacrifices accuracy for speed.
Parameters:

value: float, -1.0 >= _value >= 1.0 range, value to test.

Returns: float

ierf_double(value) computes the inverse error function using the Newton method with double refinement.
Parameters:

value: float, -1. > _value > 1. range, _value to test.

Returns: float

ierf(value) computes the inverse error function using the Newton method.
Parameters:

value: float, -1. > _value > 1. range, _value to test.

Returns: float

complement(probability) probability that the event will not occur.
Parameters:

probability: float, 0 >=_p >= 1, probability of event.

Returns: float

entropy_gini_impurity_single(probability) Gini Inbalance or Gini index for a given probability.
Parameters:

probability: float, 0>=x>=1, probability of event.

Returns: float

entropy_gini_impurity(events) Gini Inbalance or Gini index for a series of events.
Parameters:

events: float[], 0>=x>=1, array with event probability's.

Returns: float

entropy_shannon_single(probability) Entropy information value of the probability of a single event.
Parameters:

probability: float, 0>=x>=1, probability value.

Returns: float, value as bits of information.

entropy_shannon(events) Entropy information value of a distribution of events.
Parameters:

events: float[], 0>=x>=1, array with probability's.

Returns: float

inequality_chebyshev(n_stdeviations) Calculates Chebyshev Inequality.
Parameters:

n_stdeviations: float, positive over or equal to 1.0

Returns: float

inequality_chebyshev_distribution(mean, std) Calculates Chebyshev Inequality.
Parameters:

mean: float, mean of a distribution
std: float, standard deviation of a distribution

Returns: float

inequality_chebyshev_sample(data_sample) Calculates Chebyshev Inequality for a array of values.
Parameters:

data_sample: float[], array of numbers.

Returns: float

intersection_of_independent_events(events) Probability that all arguments will happen when neither outcome
is affected by the other (accepts 1 or more arguments)
Parameters:

events: float[], 0 >= _p >= 1, list of event probabilities.

Returns: float

union_of_independent_events(events) Probability that either one of the arguments will happen when neither outcome
is affected by the other (accepts 1 or more arguments)
Parameters:

events: float[], 0 >= _p >= 1, list of event probabilities.

Returns: float

mass_function(sample, n_bins) Probabilities for each bin in the range of sample.
Parameters:

sample: float[], samples to pool probabilities.
n_bins: int, number of bins to split the range
return float[]

cumulative_distribution_function(mean, stdev, value) Use the CDF to determine the probability that a random observation
that is taken from the population will be less than or equal to a certain value.
Or returns the area of probability for a known value in a normal distribution.
Parameters:

mean: float, samples to pool probabilities.
stdev: float, number of bins to split the range
value: float, limit at which to stop.

Returns: float

transition_matrix(distribution) Transition matrix for the suplied distribution.
Parameters:

distribution: float[], array with probability distribution. ex:. [0.25, 0.50, 0.25]

Returns: float[]

diffusion_matrix(transition_matrix, dimension, target_step) Probability of reaching target_state at target_step after starting from start_state
Parameters:

transition_matrix: float[], "pseudo2d" probability transition matrix.
dimension: int, size of the matrix dimension.
target_step: number of steps to find probability.

Returns: float[]

state_at_time(transition_matrix, dimension, start_state, target_state, target_step) Probability of reaching target_state at target_step after starting from start_state
Parameters:

transition_matrix: float[], "pseudo2d" probability transition matrix.
dimension: int, size of the matrix dimension.
start_state: state at which to start.
target_state: state to find probability.
target_step: number of steps to find probability.

Release Notes

v2
- general update on descriptions.
- update to support builtin matrices.
- fixed a mistake on the label/test code.

Pine library

In true TradingView spirit, the author has published this Pine code as an open-source library so that other Pine programmers from our community can reuse it. Cheers to the author! You may use this library privately or in other open-source publications, but reuse of this code in a publication is governed by House rules.

RicardoSantos

Disclaimer

The information and publications are not meant to be, and do not constitute, financial, investment, trading, or other types of advice or recommendations supplied or endorsed by TradingView. Read more in the Terms of Use.