API Reference

calc_rtac_n(x, y, coverage_factor=1.0)

Calculates for .

Parameters:
  • x –

    A numpy.ndarray with shape (n,).

  • y –

    A numpy.ndarray with shape (n,).

  • coverage_factor –

    A positive float.
Returns:
  • float –

    .
Source code in rtacpy/calc_rtac_n.py 
@njit
def calc_rtac_n(x,y,coverage_factor=1.0):
    '''Calculates \(\text{RTAC}_n(S_n, \\text{coverage_factor})\) for \(S_n:=\{(x_i, y_i)\}_{i=1}^n\).

    :param x: A numpy.ndarray with shape (n,).
    :param y: A numpy.ndarray with shape (n,).
    :param coverage_factor: A positive float.
    :return: \(\text{RTAC}_n(S_n, \\text{coverage_factor})\).
    :rtype: float
    '''
    n = len(x)
    edge_length = np.sqrt(coverage_factor/n)
    RTA_n = calc_rta_n(x, y, edge_length=edge_length)
    alpha_n = calc_alpha_n(n, edge_length)
    rtac_n = 1 - ((RTA_n - alpha_n)/(1-np.exp(-coverage_factor)-alpha_n))
    return rtac_n

area_coverage_independence_test(x, y, coverage_factor=1, null_dist=None)

Calculates and its p value for the given sample .

Parameters:
  • x –

    A numpy.ndarray with shape (n,).

  • y –

    A numpy.ndarray with shape (n,).

  • coverage_factor –

    A positive float.

  • null_dist –

    Optional. A numpy.ndarray with shape (N,) with samples of under the null hypothesis of independence. If not supplied, a null distribution will be computed ad-hoc.
Returns:
  • (float, float) –

    (, p value)
Source code in rtacpy/independence_test.py 
def area_coverage_independence_test(x, y, coverage_factor=1, null_dist=None):
    '''Calculates \(\text{RTAC}_n(S_n, \\text{coverage_factor})\) and its p value for the given sample \(S_n:=\{(x_i, y_i)\}_{i=1}^n\).

    :param x: A numpy.ndarray with shape (n,).
    :param y: A numpy.ndarray with shape (n,).
    :param coverage_factor: A positive float.
    :param null_dist: Optional. A numpy.ndarray with shape (N,) with samples of \(\text{RTAC}_n\) under the null hypothesis of independence. If not supplied, a null distribution will be computed ad-hoc.
    :return: (\(\text{RTAC}_n(S_n, \\text{coverage_factor})\), p value)
    :rtype: (float, float)
    '''
    null_dist = null_dist if null_dist is not None else create_null_dist(len(x), coverage_factor)
    rtac_n = calc_rtac_n(x,y,coverage_factor)
    return rtac_n, calc_p_value(rtac_n, null_dist)

calc_p_value(rtac_n, null_dist)

Calculates the p value of a given value of against a given distribution under the null hypothesis.

Parameters:
  • rtac_n –

    float, to calculate a p value for.

  • null_dist –

    A numpy.ndarray with shape (N,) with samples of under the null hypothesis of independence.
Returns:
  • float –

    The p value of the given according to the given distribution under the null.
Source code in rtacpy/independence_test.py 
def calc_p_value(rtac_n, null_dist):
    '''Calculates the p value of a given value of \(\text{RTAC}_n\) against a given distribution under the null hypothesis.

    :param rtac_n: float, \(\text{RTAC}_n\) to calculate a p value for.
    :param null_dist: A numpy.ndarray with shape (N,) with samples of \(\text{RTAC}_n\) under the null hypothesis of independence.
    :return: The p value of the given \(\text{RTAC}_n\) according to the given distribution under the null.
    :rtype: float
    '''
    return (rtac_n<null_dist).mean()

create_null_dist(n, coverage_factor=1, num_samples=2000)

Calculates the distribution of under the null hypothesis of independence, for given values of n and coverage_factor.

Parameters:
  • n –

    A positive integer, the sample size for each calculation of .

  • coverage_factor –

    A positive float, the coverage factor to be used for each calculation of .

  • num_samples –

    The number of samples to be included in the null distribution.
Returns:
  • numpy.ndarray –

    A numpy array of shape (num_samples,) with i.i.d samples of under the null hypothesis.
Source code in rtacpy/independence_test.py 
@njit
def create_null_dist(n, coverage_factor=1, num_samples=2000):
    '''Calculates the distribution of \(\text{RTAC}_n\) under the null hypothesis of independence, for given values of n and coverage_factor.

    :param n: A positive integer, the sample size for each calculation of \(\text{RTAC}_n\).
    :param coverage_factor: A positive float, the coverage factor to be used for each calculation of \(\text{RTAC}_n\).
    :param num_samples: The number of samples to be included in the null distribution.
    :return: A numpy array of shape (num_samples,) with i.i.d samples of \(\text{RTAC}_n\) under the null hypothesis.
    :rtype: numpy.ndarray
    '''
    return np.array([calc_rtac_n(np.random.rand(n), np.random.rand(n), coverage_factor) for _ in range(num_samples)])