# Probability

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:.
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.

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.

Disclaimer

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