**"Probability"**

**erf(value)**Complementary error function

Parameters:

**value**: float, value to test.

**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.

**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.

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

Parameters:

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

**complement(probability)**probability that the event will not occur.

Parameters:

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

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

Parameters:

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

**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.

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

Parameters:

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

**entropy_shannon(events)**Entropy information value of a distribution of events.

Parameters:

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

**inequality_chebyshev(n_stdeviations)**Calculates Chebyshev Inequality.

Parameters:

**n_stdeviations**: float, positive over or equal to 1.0

**inequality_chebyshev_distribution(mean, std)**Calculates Chebyshev Inequality.

Parameters:

**mean**: float, mean of a distribution

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

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

Parameters:

**data_sample**: float, array of numbers.

**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.

**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.

**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.

**transition_matrix(distribution)**Transition matrix for the suplied distribution.

Parameters:

**distribution**: float, array with probability distribution. ex:.

**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.

**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.