def summarize(data,
avg=('amean', 'gmean', 'median', 'mode'),
ci_level=0.95,
bandwidth='silverman',
precision=0.1):
""" Estimate different grain size statistics. This includes different means,
the median, the frequency peak grain size via KDE, the confidence intervals
using different methods, and the distribution features.
Parameters
----------
data : array_like
the size of the grains
avg : string, tuple or list; optional
the averages to be estimated
| Types:
| 'amean' - arithmetic mean
| 'gmean' - geometric mean
| 'median' - median
| 'mode' - the kernel-based frequency peak of the distribution
ci_level : scalar between 0 and 1; optional
the certainty of the confidence interval (default = 0.95)
bandwidth : string {'silverman' or 'scott'} or positive scalar; optional
the method to estimate the bandwidth or a scalar directly defining the
bandwidth. It uses the Silverman plug-in method by default.
precision : positive scalar or None; optional
the maximum precision expected for the "peak" kde-based estimator.
Default is 0.1. Note that this is not related with the confidence
intervals
Call functions
--------------
- amean, gmean, median, and freq_peak (from averages)
Examples
--------
>>> summarize(dataset['diameters'])
>>> summarize(dataset['diameters'], ci_level=0.99)
>>> summarize(np.log(dataset['diameters']), avg=('amean', 'median', 'mode'))
Returns
-------
None
"""
# remove missing and infinite values
data = data[~np.isnan(data) & ~np.isinf(data)]
# check for negative values and remove
if data[data <= 0].size > 0:
print(
'Warning: There were negative and/or zero values in your dataset!')
data = data[data > 0]
print('Negative/zero values were automatically removed')
print('')
# estimate Shapiro-Wilk test to check normality and lognormality
# In Shapiro-Wilk tests, the chances of the null hypothesis being
# rejected becomes larger for large sample sizes. We limit the
# sample size to a maximum of 250
if len(data) > 250:
W, p_value = shapiro(np.random.choice(data, size=250))
W2, p_value2 = shapiro(np.random.choice(np.log(data), size=250))
else:
W, p_value = shapiro(data)
W2, p_value2 = shapiro(np.log(data))
if 'amean' in avg:
if p_value2 < 0.05:
amean, __, ci, length = averages.amean(data,
ci_level,
method='ASTM')
else:
if len(data) > 99:
amean, __, (low_ci,
high_ci), length2 = averages.amean(data,
ci_level,
method='mCox')
else:
amean, __, (low_ci,
high_ci), length2 = averages.amean(data,
ci_level,
method='GCI')
# estimate coefficients of variation
lower_cvar = 100 * (amean - low_ci) / amean
upper_cvar = 100 * (high_ci - amean) / amean
print(' ')
print(
'============================================================================'
)
print('CENTRAL TENDENCY ESTIMATORS')
print(
'============================================================================'
)
print(f'Arithmetic mean = {amean:0.2f} microns')
print(f'Confidence intervals at {ci_level * 100:0.1f} %')
if p_value2 < 0.05:
print(
f'CLT (ASTM) method: {ci[0]:0.2f} - {ci[1]:0.2f}, (±{100 * (ci[1] - amean) / amean:0.1f}%), length = {length:0.3f}'
)
else:
if len(data) > 99:
print(
f'mCox method: {low_ci:0.2f} - {high_ci:0.2f} (-{lower_cvar:0.1f}%, +{upper_cvar:0.1f}%), length = {length2:0.3f}'
)
else:
print(
f'GCI method: {low_ci:0.2f} - {high_ci:0.2f} (-{lower_cvar:0.1f}%, +{upper_cvar:0.1f}%), length = {length2:0.3f}'
)
if 'gmean' in avg:
m = 'CLT' if len(
data
) > 99 else 'bayes' # choose optimal method to estimate confidence intervals
gmean, msd, (low_ci, high_ci), length = averages.gmean(data,
ci_level,
method=m)
# estimate coefficients of variation
lower_cvar = 100 * (gmean - low_ci) / gmean
upper_cvar = 100 * (high_ci - gmean) / gmean
print(
'============================================================================'
)
print(f'Geometric mean = {gmean:0.2f} microns')
print(f'Confidence interval at {ci_level * 100:0.1f} %')
print(
f'{m} method: {low_ci:0.2f} - {high_ci:0.2f} (-{lower_cvar:0.1f}%, +{upper_cvar:0.1f}%), length = {length:0.3f}'
)
if 'median' in avg:
median, iqr, (low_ci,
high_ci), length = averages.median(data, ci_level)
# estimate coefficients of variation
lower_cvar = 100 * (median - low_ci) / median
upper_cvar = 100 * (high_ci - median) / median
print(
'============================================================================'
)
print(f'Median = {median:0.2f} microns')
print(f'Confidence interval at {ci_level * 100:0.1f} %')
print(
f'robust method: {low_ci:0.2f} - {high_ci:0.2f} (-{lower_cvar:0.1f}%, +{upper_cvar:0.1f}%), length = {length:0.3f}'
)
if 'mode' in avg:
__, mode, __, bw = averages.freq_peak(data, bandwidth, precision)
print(
'============================================================================'
)
print(f'Mode (KDE-based) = {mode:0.2f} microns')
print(f'Maximum precision set to {precision}')
if type(bandwidth) is str:
print(f'KDE bandwidth = {bw} ({bandwidth} rule)')
else:
print(f'KDE bandwidth = {bandwidth}')
print(' ')
print(
'============================================================================'
)
print('DISTRIBUTION FEATURES')
print(
'============================================================================'
)
print(f'Sample size (n) = {len(data)}')
print(f'Standard deviation = {np.std(data):0.2f} (1-sigma)')
if 'median' in avg:
print(f'Interquartile range (IQR) = {iqr:0.2f}')
if 'gmean' in avg:
print(
f'Lognormal shape (Multiplicative Standard Deviation) = {msd:0.2f}'
)
print(
'============================================================================'
)
print('Shapiro-Wilk test warnings:')
if p_value < 0.05:
print('Data is not normally distributed!')
print(
f'Normality test: {W:0.2f}, {p_value:0.2f} (test statistic, p-value)'
)
if p_value2 < 0.05:
print('Data is not lognormally distributed!')
print(
f'Lognormality test: {W2:0.2f}, {p_value2:0.2f} (test statistic, p-value)'
)
print(
'============================================================================'
)
return None
def test_median_known_value(self):
"""median should return known value from known input list."""
for nums, value in self.known_medians:
result = averages.median(nums)
self.assertEqual(value, result)
import averages print(averages.mean(1, 5, 1)) print(averages.median(1, 5, 1)) print(averages.rms(1, 5, 1)) print(averages.middle_average(1, 5, 1))