Module stat: helper functions for processing statistics

Package teneva, module stat: helper functions for processing statistics.

This module contains the helper functions for processing statistics, including computation of the CDF function and its confidence bounds.

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teneva.stat.cdf_confidence(x, alpha=0.05)

Construct a Dvoretzky-Kiefer-Wolfowitz confidence band for the CDF.

Parameters:

• x (np.ndarray) – the empirical distribution in the form of 1D np.ndarray of length m.

• alpha (float) – alpha for the (1 - alpha) confidence band.

Returns:

CDF lower and upper bounds in the form of 1D np.ndarray of the length m.

Return type:

(np.ndarray, np.ndarray)

Examples:

# Statistical points:
points = np.random.randn(15)

# Compute the confidence:
cdf_min, cdf_max = teneva.cdf_confidence(points)
for p, c_min, c_max in zip(points, cdf_min, cdf_max):
    print(f'{p:-8.4f} | {c_min:-8.4f} | {c_max:-8.4f}')

# >>> ----------------------------------------
# >>> Output:

#   0.4967 |   0.1461 |   0.8474
#  -0.1383 |   0.0000 |   0.2124
#   0.6477 |   0.2970 |   0.9983
#   1.5230 |   1.0000 |   1.0000
#  -0.2342 |   0.0000 |   0.1165
#  -0.2341 |   0.0000 |   0.1165
#   1.5792 |   1.0000 |   1.0000
#   0.7674 |   0.4168 |   1.0000
#  -0.4695 |   0.0000 |   0.0000
#   0.5426 |   0.1919 |   0.8932
#  -0.4634 |   0.0000 |   0.0000
#  -0.4657 |   0.0000 |   0.0000
#   0.2420 |   0.0000 |   0.5926
#  -1.9133 |   0.0000 |   0.0000
#  -1.7249 |   0.0000 |   0.0000
#

teneva.stat.cdf_getter(x)

Build the getter for CDF.

Parameters:

x (list or np.ndarray) – one-dimensional points.

Returns:

the function that computes CDF values. Its input may be one point (float) or a set of points (1D np.ndarray). The output (corresponding CDF value/values) will have the same type.

Return type:

function

Examples:

# Statistical points:
x = np.random.randn(1000)

# Build the CDF getter:
cdf = teneva.cdf_getter(x)

z = -9999  # Point for CDF computations

cdf(z)

# >>> ----------------------------------------
# >>> Output:

# 0.0
#

z = +9999  # Point for CDF computations

cdf(z)

# >>> ----------------------------------------
# >>> Output:

# 1.0
#

# Several points for CDF computations:
z = [-10000, -10, -1, 0, 100]

cdf(z)

# >>> ----------------------------------------
# >>> Output:

# array([0.   , 0.   , 0.145, 0.485, 1.   ])
#