RNG 1.4.0

Python3 API for the C++ Random library

RNG Engine for Python

Python3 interface to the c++ random library

Designed for python developers familiar with the c++ random header

Sister Projects:

• Fortuna: Collection of abstractions to make custom random value generators. https://pypi.org/project/Fortuna/
• Pyewacket: Complete drop-in replacement for the Python3 Random Module. https://pypi.org/project/Pyewacket/

Support these and other random projects: https://www.patreon.com/brokencode

Warning: RNG is not suitable for cryptography or secure hashing.

Quick Install for Mac and Linux: $ pip install RNG, import RNG as needed.

---

Random Generator Signatures

Random Boolean Variates

• bernoulli_distribution(ratio_of_truth) -> bool

Random Integer Variates

• uniform_int_distribution(left_limit: int, right_limit: int) -> int
• binomial_distribution(number_of_trials: int, probability: float) -> int
• negative_binomial_distribution(number_of_trials: int, probability: float) -> int
• geometric_distribution(probability: float) -> int
• poisson_distribution(mean: float) -> int

Random Float Variates

• generate_canonical() -> float
• uniform_real_distribution(left_limit: float, right_limit: float) -> float
• exponential_distribution(lambda_rate: float) -> float
• gamma_distribution(shape: float, scale: float) -> float
• weibull_distribution(shape: float, scale: float) -> float
• normal_distribution(mean: float, std_dev: float) -> float
• lognormal_distribution(log_mean: float, log_deviation: float) -> float
• extreme_value_distribution(location: float, scale: float) -> float
• chi_squared_distribution(degrees_of_freedom: float) -> float
• cauchy_distribution(location: float, scale: float) -> float
• fisher_f_distribution(degrees_of_freedom_1: float, degrees_of_freedom_2: float) -> float
• student_t_distribution(degrees_of_freedom: float) -> float

Random Generator Specifications

Random Boolean

• bernoulli_distribution(ratio_of_truth: float) -> bool
  • Bernoulli distribution.
  • @param ratio_of_truth :: the probability of True. Expected input range: [0.0, 1.0], clamped.
  • @return :: True or False

$ python3
Python 3.7.3
>>> import RNG

>>> RNG.bernoulli_distribution(1.0)
True
>>> RNG.bernoulli_distribution(0.0)
False

>>> RNG.distribution(RNG.bernoulli_distribution, 1/3)
Statistics of 1000 Samples:
 Minimum: False
 Median: False
 Maximum: True
 Mean: 0.368
 Std Deviation: 0.4825026516080599
Distribution of 10000 Samples:
 False: 66.73%
 True: 33.27%

>>> RNG.distribution(RNG.bernoulli_distribution, 2/3)
Statistics of 1000 Samples:
 Minimum: False
 Median: True
 Maximum: True
 Mean: 0.659
 Std Deviation: 0.47428255707325345
Distribution of 10000 Samples:
 False: 33.65%
 True: 66.35%

Random Integer

• uniform_int_distribution(left_limit: int, right_limit: int) -> int
  • Flat uniform distribution.
  • 20x faster than random.randint()
  • @param left_limit :: input A.
  • @param right_limit :: input B.
  • @return :: random integer in the inclusive range [A, B] or [B, A] if B < A

$ python3
Python 3.7.3
>>> import RNG
>>> RNG.uniform_int_distribution(1, 100)
42
>>> RNG.distribution(RNG.uniform_int_distribution, 1, 10)
Statistics of 1000 Samples:
 Minimum: 1
 Median: 6
 Maximum: 10
 Mean: 5.456
 Std Deviation: 2.881730099847723
Distribution of 10000 Samples:
 1: 10.14%
 2: 9.48%
 3: 9.82%
 4: 10.28%
 5: 10.14%
 6: 9.91%
 7: 9.94%
 8: 9.66%
 9: 10.49%
 10: 10.14%

>>> RNG.distribution(RNG.uniform_int_distribution, 10, 1)
Statistics of 1000 Samples:
 Minimum: 1
 Median: 6
 Maximum: 10
 Mean: 5.513
 Std Deviation: 2.8106459632495038
Distribution of 10000 Samples:
 1: 10.01%
 2: 10.17%
 3: 10.36%
 4: 9.84%
 5: 9.62%
 6: 9.91%
 7: 10.36%
 8: 9.8%
 9: 9.93%
 10: 10.0%

• RNG.binomial_distribution(number_of_trials: int, probability: float) -> int
  • Based on the idea of flipping a coin and counting how many heads come up after some number of flips.
  • @param number_of_trials :: how many times to flip a coin.
  • @param probability :: how likely heads will be flipped. 0.5 is a fair coin. 1.0 is a double headed coin.
  • @return :: count of how many heads came up.
• RNG.negative_binomial_distribution(trial_successes: int, probability: float) -> int
  • Based on the idea of flipping a coin as long as it takes to succeed.
  • @param trial_successes :: the required number of heads flipped to succeed.
  • @param probability :: how likely heads will be flipped. 0.50 is a fair coin.
  • @return :: the count of how many tails came up before the required number of heads.
• RNG.geometric_distribution(probability: float) -> int
  • Same as random_negative_binomial(1, probability).
• RNG.poisson_distribution(mean: float) -> int
  • @param mean :: sets the average output of the function.
  • @return :: random integer, poisson distribution centered on the mean.

Random Floating Point

• RNG.generate_canonical() -> float
  • Evenly distributes real values of maximum precision.
  • @return :: random Float in range {0.0, 1.0} biclusive. The spec defines the output range to be [0.0, 1.0).
    • biclusive: feature/bug rendering the exclusivity of this function a bit more mysterious than desired. This is a known compiler bug.
• RNG.uniform_real_distribution(left_limit: float, right_limit: float) -> float
  • Suffers from the same biclusive feature/bug noted for generate_canonical().
  • @param left_limit :: input A
  • @param right_limit :: input B
  • @return :: random Float in range {A, B} biclusive. The spec defines the output range to be [A, B).
• RNG.normal_distribution(mean: float, std_dev: float) -> float
  • @param mean :: sets the average output of the function.
  • @param std_dev :: standard deviation. Specifies spread of data from the mean.
• RNG.lognormal_distribution(log_mean: float, log_deviation: float) -> float
  • @param log_mean :: sets the log of the mean of the function.
  • @param log_deviation :: log of the standard deviation. Specifies spread of data from the mean.
• RNG.exponential_distribution(lambda_rate: float) -> float
  • Produces random non-negative floating-point values, distributed according to probability density function.
  • @param lambda_rate :: λ constant rate of a random event per unit of time/distance.
  • @return :: The time/distance until the next random event. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.
• RNG.gamma_distribution(shape: float, scale: float) -> float
  • Generalization of the exponential distribution.
  • Produces random positive floating-point values, distributed according to probability density function.
  • @param shape :: α the number of independent exponentially distributed random variables.
  • @param scale :: β the scale factor or the mean of each of the distributed random variables.
  • @return :: the sum of α independent exponentially distributed random variables, each of which has a mean of β.
• RNG.weibull_distribution(shape: float, scale: float) -> float
  • Generalization of the exponential distribution.
  • Similar to the gamma distribution but uses a closed form distribution function.
  • Popular in reliability and survival analysis.
• RNG.extreme_value_distribution(location: float, scale: float) -> float
  • Based on Extreme Value Theory.
  • Used for statistical models of the magnitude of earthquakes and volcanoes.
• RNG.chi_squared_distribution(degrees_of_freedom: float) -> float
  • Used with the Chi Squared Test and Null Hypotheses to test if sample data fits an expected distribution.
• RNG.cauchy_distribution(location: float, scale: float) -> float
  • @param location :: It specifies the location of the peak. The default value is 0.0.
  • @param scale :: It represents the half-width at half-maximum. The default value is 1.0.
  • @return :: Continuous Distribution.
• RNG.fisher_f_distribution(degrees_of_freedom_1: float, degrees_of_freedom_2: float) -> float
  • F distributions often arise when comparing ratios of variances.
• RNG.student_t_distribution(degrees_of_freedom: float) -> float
  • T distribution. Same as a normal distribution except it uses the sample standard deviation rather than the population standard deviation.
  • As degrees_of_freedom goes to infinity it converges with the normal distribution.

Distribution & Performance Test Suite

• RNG.timer(func: staticmethod, *args, **kwargs) -> None
  • For temporal analysis of non-deterministic functions.
  • @param func :: Function, method or lambda to analyze. func(*args, **kwargs)
• RNG.distribution(func: staticmethod, *args, **kwargs) -> None
  • For statistical analysis of non-deterministic functions.
  • @param func :: Function, method or lambda to analyze. func(*args, **kwargs)
• RNG.distribution_timer(func: staticmethod, *args, **kwargs) -> None
  • For statistical and temporal analysis of non-deterministic functions.
  • @param func :: Function, method or lambda to analyze. func(*args, **kwargs)
  • @optional_kw num_cycles :: Total number of samples for distribution analysis, statistical analysis is limited to the first 1000 samples, timing estimates are handled separately.
  • @optional_kw post_processor :: Used to scale a large set of data into a smaller set of groupings, this function is invoked on the output and collated after the stats battery.
• RNG.quick_test() -> None
  • Runs a quick battery of tests for every function in the module.

Development Log

RNG 1.4.0

• API Refactoring

RNG 1.3.4

• Storm Update 3.1.1

RNG 1.3.3

• Installer script update

RNG 1.3.2

• Minor Bug Fix

RNG 1.3.1

• Test Update

RNG 1.3.1

• Fixed Typos

RNG 1.3.0

• Storm Update

RNG 1.2.5

• Low level clean up

RNG 1.2.4

• Minor Typos Fixed

RNG 1.2.3

• Documentation Update
• Test Update
• Bug Fixes

RNG 1.0.0 - 1.2.2, internal

• API Changes:
  • randint changed to random_int
  • randbelow changed to random_below
  • random changed to generate_canonical
  • uniform changed to random_float

RNG 0.2.3

• Bug Fixes

RNG 0.2.2

• discrete() removed.

RNG 0.2.1

• minor typos
• discrete() depreciated.

RNG 0.2.0

• Major Rebuild.

RNG 0.1.22

• The RNG Storm Engine is now the default standard.
• Experimental Vortex Engine added for testing.

RNG 0.1.21 beta

• Small update to the testing suite.

RNG 0.1.20 beta

• Changed default inputs for random_int and random_below to sane values.
  • random_int(left_limit=1, right_limit=20) down from -2**63, 2**63 - 1
  • random_below(upper_bound=10) down from 2**63 - 1

RNG 0.1.19 beta

• Broke some fixed typos, for a change of pace.

RNG 0.1.18 beta

• Fixed some typos.

RNG 0.1.17 beta

• Major Refactoring.
• New primary engine: Hurricane.
• Experimental engine Typhoon added: random_below() only.

RNG 0.1.16 beta

• Internal Engine Performance Tuning.

RNG 0.1.15 beta

• Engine Testing.

RNG 0.1.14 beta

• Fixed a few typos.

RNG 0.1.13 beta

• Fixed a few typos.

RNG 0.1.12 beta

• Major Test Suite Upgrade.
• Major Bug Fixes.
  • Removed several 'foot-guns' in prep for fuzz testing in future releases.

RNG 0.1.11 beta

• Fixed small bug in the install script.

RNG 0.1.10 beta

• Fixed some typos.

RNG 0.1.9 beta

• Fixed some typos.

RNG 0.1.8 beta

• Fixed some typos.
• More documentation added.

RNG 0.1.7 beta

• The random_floating_point function renamed to random_float.
• The function c_rand() has been removed as well as all the cruft it required.
• Major Documentation Upgrade.
• Fixed an issue where keyword arguments would fail to propagate. Both, positional args and kwargs now work as intended.
• Added this Dev Log.

RNG 0.0.6 alpha

• Minor ABI changes.

RNG 0.0.5 alpha

• Tests redesigned slightly for Float functions.

RNG 0.0.4 alpha

• Random Float Functions Implemented.

RNG 0.0.3 alpha

• Random Integer Functions Implemented.

RNG 0.0.2 alpha

• Random Bool Function Implemented.

RNG 0.0.1 pre-alpha

• Planning & Design.

Distribution and Performance Test Suite

Quick Test: RNG Storm Engine
=========================================================================

Boolean Distribution Variates

Output Analysis: bernoulli_distribution(0.3333333333333333)
Typical Timing: 63 ± 1 ns
Statistics of 1024 samples:
 Minimum: False
 Median: False
 Maximum: True
 Mean: 0.3349609375
 Std Deviation: 0.47220743494806877
Distribution of 10240 samples:
 False: 66.962890625%
 True: 33.037109375%

Output Analysis: bernoulli_distribution(0.6666666666666666)
Typical Timing: 63 ± 1 ns
Statistics of 1024 samples:
 Minimum: False
 Median: True
 Maximum: True
 Mean: 0.6552734375
 Std Deviation: 0.47551127337020155
Distribution of 10240 samples:
 False: 32.275390625%
 True: 67.724609375%


Integer Distribution Variates

Base Case
Output Analysis: Random.randint(1, 6)
Typical Timing: 1125 ± 19 ns
Statistics of 1024 samples:
 Minimum: 1
 Median: 4
 Maximum: 6
 Mean: 3.5625
 Std Deviation: 1.7147511354422509
Distribution of 10240 samples:
 1: 16.728515625%
 2: 16.708984375%
 3: 16.03515625%
 4: 16.23046875%
 5: 17.001953125%
 6: 17.294921875%

Output Analysis: uniform_int_distribution(1, 6)
Typical Timing: 63 ± 12 ns
Statistics of 1024 samples:
 Minimum: 1
 Median: 3
 Maximum: 6
 Mean: 3.4921875
 Std Deviation: 1.673769079816962
Distribution of 10240 samples:
 1: 16.62109375%
 2: 16.494140625%
 3: 16.640625%
 4: 17.412109375%
 5: 16.572265625%
 6: 16.259765625%

Output Analysis: binomial_distribution(4, 0.5)
Typical Timing: 157 ± 1 ns
Statistics of 1024 samples:
 Minimum: 0
 Median: 2
 Maximum: 4
 Mean: 1.9599609375
 Std Deviation: 0.9942937872304264
Distribution of 10240 samples:
 0: 6.435546875%
 1: 24.7265625%
 2: 37.431640625%
 3: 25.37109375%
 4: 6.03515625%

Output Analysis: negative_binomial_distribution(5, 0.75)
Typical Timing: 125 ± 6 ns
Statistics of 1024 samples:
 Minimum: 0
 Median: 1
 Maximum: 8
 Mean: 1.7099609375
 Std Deviation: 1.510102311643158
Distribution of 10240 samples:
 0: 24.052734375%
 1: 29.35546875%
 2: 22.529296875%
 3: 13.291015625%
 4: 5.986328125%
 5: 2.7734375%
 6: 1.25%
 7: 0.52734375%
 8: 0.15625%
 9: 0.048828125%
 10: 0.01953125%
 12: 0.009765625%

Output Analysis: geometric_distribution(0.75)
Typical Timing: 63 ± 1 ns
Statistics of 1024 samples:
 Minimum: 0
 Median: 0
 Maximum: 4
 Mean: 0.2998046875
 Std Deviation: 0.6086376956069064
Distribution of 10240 samples:
 0: 75.78125%
 1: 18.486328125%
 2: 4.4140625%
 3: 0.95703125%
 4: 0.2734375%
 5: 0.087890625%

Output Analysis: poisson_distribution(4.5)
Typical Timing: 94 ± 6 ns
Statistics of 1024 samples:
 Minimum: 0
 Median: 4
 Maximum: 15
 Mean: 4.6005859375
 Std Deviation: 2.2177722674656404
Distribution of 10240 samples:
 0: 0.986328125%
 1: 4.90234375%
 2: 10.9375%
 3: 17.275390625%
 4: 18.6328125%
 5: 16.73828125%
 6: 12.470703125%
 7: 8.671875%
 8: 4.90234375%
 9: 2.607421875%
 10: 1.123046875%
 11: 0.537109375%
 12: 0.13671875%
 13: 0.048828125%
 14: 0.01953125%
 15: 0.009765625%


Floating Point Distribution Variates

Base Case
Output Analysis: Random.random()
Typical Timing: 32 ± 16 ns
Statistics of 1024 samples:
 Minimum: 0.00032892642793780347
 Median: (0.4894346962693171, 0.4898661803837664)
 Maximum: 0.9990303489773977
 Mean: 0.48990903122609464
 Std Deviation: 0.2877923204977123
Post-processor distribution of 10240 samples using round method:
 0: 50.21484375%
 1: 49.78515625%

Output Analysis: generate_canonical()
Typical Timing: 32 ± 16 ns
Statistics of 1024 samples:
 Minimum: 0.0008802851804854906
 Median: (0.5239102176773246, 0.5245990843200793)
 Maximum: 0.9982303174860803
 Mean: 0.5096530375857149
 Std Deviation: 0.28789444569003747
Post-processor distribution of 10240 samples using round method:
 0: 49.8828125%
 1: 50.1171875%

Output Analysis: uniform_real_distribution(0.0, 10.0)
Typical Timing: 32 ± 15 ns
Statistics of 1024 samples:
 Minimum: 0.004116377520471437
 Median: (4.881844004595013, 4.891818588700552)
 Maximum: 9.995091346151177
 Mean: 4.969692806231672
 Std Deviation: 2.957758167769482
Post-processor distribution of 10240 samples using floor method:
 0: 10.009765625%
 1: 10.390625%
 2: 10.244140625%
 3: 9.853515625%
 4: 9.6484375%
 5: 9.74609375%
 6: 10.21484375%
 7: 9.70703125%
 8: 10.078125%
 9: 10.107421875%

Base Case
Output Analysis: Random.expovariate(1.0)
Typical Timing: 313 ± 12 ns
Statistics of 1024 samples:
 Minimum: 0.0016695808311731676
 Median: (0.7323344388886976, 0.7338114824809282)
 Maximum: 7.254103481579576
 Mean: 1.0164870131624548
 Std Deviation: 0.9713831502877656
Post-processor distribution of 10240 samples using floor method:
 0: 63.30078125%
 1: 22.98828125%
 2: 8.75%
 3: 3.2421875%
 4: 1.11328125%
 5: 0.390625%
 6: 0.126953125%
 7: 0.05859375%
 8: 0.01953125%
 9: 0.009765625%

Output Analysis: exponential_distribution(1.0)
Typical Timing: 63 ± 1 ns
Statistics of 1024 samples:
 Minimum: 0.0012632597757556792
 Median: (0.6600052912812918, 0.6613695458651184)
 Maximum: 8.233845647085891
 Mean: 1.00610754274133
 Std Deviation: 1.0321380206943058
Post-processor distribution of 10240 samples using floor method:
 0: 63.154296875%
 1: 22.841796875%
 2: 8.681640625%
 3: 3.427734375%
 4: 1.171875%
 5: 0.517578125%
 6: 0.146484375%
 7: 0.029296875%
 8: 0.029296875%

Base Case
Output Analysis: Random.gammavariate(1.0, 1.0)
Typical Timing: 469 ± 10 ns
Statistics of 1024 samples:
 Minimum: 0.00046802738052935226
 Median: (0.6821019599683634, 0.6827638257599115)
 Maximum: 8.239563570307116
 Mean: 0.991191663612758
 Std Deviation: 0.992752118351304
Post-processor distribution of 10240 samples using floor method:
 0: 63.369140625%
 1: 23.203125%
 2: 8.740234375%
 3: 2.939453125%
 4: 1.1328125%
 5: 0.400390625%
 6: 0.15625%
 7: 0.0390625%
 8: 0.009765625%
 9: 0.009765625%

Output Analysis: gamma_distribution(1.0, 1.0)
Typical Timing: 63 ± 6 ns
Statistics of 1024 samples:
 Minimum: 0.0014657259682512246
 Median: (0.6653115966948129, 0.6693656541028595)
 Maximum: 6.991985618991515
 Mean: 0.9709175408169873
 Std Deviation: 0.9725555195269021
Post-processor distribution of 10240 samples using floor method:
 0: 63.466796875%
 1: 22.958984375%
 2: 8.57421875%
 3: 3.134765625%
 4: 1.1328125%
 5: 0.390625%
 6: 0.205078125%
 7: 0.068359375%
 8: 0.01953125%
 9: 0.029296875%
 10: 0.01953125%

Base Case
Output Analysis: Random.weibullvariate(1.0, 1.0)
Typical Timing: 407 ± 11 ns
Statistics of 1024 samples:
 Minimum: 0.00011677270768333428
 Median: (0.7373356281910795, 0.7377742027617761)
 Maximum: 7.273405612985203
 Mean: 1.064728203818245
 Std Deviation: 1.0665548207068112
Post-processor distribution of 10240 samples using floor method:
 0: 62.94921875%
 1: 23.056640625%
 2: 9.31640625%
 3: 2.900390625%
 4: 1.15234375%
 5: 0.44921875%
 6: 0.126953125%
 7: 0.029296875%
 8: 0.009765625%
 11: 0.009765625%

Output Analysis: weibull_distribution(1.0, 1.0)
Typical Timing: 94 ± 13 ns
Statistics of 1024 samples:
 Minimum: 0.0006682281416215072
 Median: (0.7053966592613788, 0.707401558275132)
 Maximum: 8.211701046521249
 Mean: 1.0350358063711198
 Std Deviation: 1.0197082661749663
Post-processor distribution of 10240 samples using floor method:
 0: 63.095703125%
 1: 23.203125%
 2: 8.6328125%
 3: 3.14453125%
 4: 1.240234375%
 5: 0.439453125%
 6: 0.107421875%
 7: 0.068359375%
 8: 0.048828125%
 9: 0.01953125%

Output Analysis: extreme_value_distribution(0.0, 1.0)
Typical Timing: 63 ± 15 ns
Statistics of 1024 samples:
 Minimum: -2.142738811035466
 Median: (0.3387893060810439, 0.348189899753224)
 Maximum: 7.010481564257828
 Mean: 0.5774527960456818
 Std Deviation: 1.273390711607122
Post-processor distribution of 10240 samples using round method:
 -2: 1.220703125%
 -1: 18.0078125%
 0: 34.912109375%
 1: 25.322265625%
 2: 12.470703125%
 3: 5.146484375%
 4: 1.9140625%
 5: 0.64453125%
 6: 0.224609375%
 7: 0.048828125%
 8: 0.05859375%
 9: 0.01953125%
 12: 0.009765625%

Base Case
Output Analysis: Random.gauss(5.0, 2.0)
Typical Timing: 563 ± 14 ns
Statistics of 1024 samples:
 Minimum: -1.2298968640837913
 Median: (4.982157926569959, 4.9846577733225965)
 Maximum: 11.542313250491487
 Mean: 4.967502708296663
 Std Deviation: 2.037834131212798
Post-processor distribution of 10240 samples using round method:
 -3: 0.009765625%
 -2: 0.087890625%
 -1: 0.29296875%
 0: 0.927734375%
 1: 2.8125%
 2: 6.4453125%
 3: 12.275390625%
 4: 17.861328125%
 5: 19.51171875%
 6: 16.93359375%
 7: 12.12890625%
 8: 6.591796875%
 9: 2.91015625%
 10: 0.869140625%
 11: 0.2734375%
 12: 0.05859375%
 13: 0.009765625%

Output Analysis: normal_distribution(5.0, 2.0)
Typical Timing: 94 ± 1 ns
Statistics of 1024 samples:
 Minimum: -1.4148021423712418
 Median: (4.903790226112948, 4.903998305344029)
 Maximum: 10.869894222069515
 Mean: 4.951246964330855
 Std Deviation: 1.989446643495987
Post-processor distribution of 10240 samples using round method:
 -3: 0.01953125%
 -2: 0.01953125%
 -1: 0.263671875%
 0: 0.91796875%
 1: 2.83203125%
 2: 6.181640625%
 3: 12.1875%
 4: 17.71484375%
 5: 19.853515625%
 6: 17.59765625%
 7: 12.001953125%
 8: 6.640625%
 9: 2.685546875%
 10: 0.849609375%
 11: 0.146484375%
 12: 0.05859375%
 13: 0.029296875%

Base Case
Output Analysis: Random.lognormvariate(1.6, 0.25)
Typical Timing: 844 ± 39 ns
Statistics of 1024 samples:
 Minimum: 2.3561313210209667
 Median: (4.93953741589801, 4.948464860488905)
 Maximum: 11.474285902742817
 Mean: 5.153628429350211
 Std Deviation: 1.3755794650586577
Post-processor distribution of 10240 samples using round method:
 2: 0.3515625%
 3: 7.9296875%
 4: 28.056640625%
 5: 30.224609375%
 6: 19.384765625%
 7: 8.90625%
 8: 3.671875%
 9: 1.064453125%
 10: 0.244140625%
 11: 0.126953125%
 12: 0.029296875%
 13: 0.009765625%

Output Analysis: lognormal_distribution(1.6, 0.25)
Typical Timing: 94 ± 14 ns
Statistics of 1024 samples:
 Minimum: 2.3134538372888387
 Median: (4.917271768022827, 4.92402996271686)
 Maximum: 12.636752519553516
 Mean: 5.110846475158034
 Std Deviation: 1.321410077828125
Post-processor distribution of 10240 samples using round method:
 2: 0.29296875%
 3: 7.822265625%
 4: 27.177734375%
 5: 30.966796875%
 6: 19.873046875%
 7: 9.013671875%
 8: 3.203125%
 9: 1.064453125%
 10: 0.390625%
 11: 0.146484375%
 12: 0.0390625%
 13: 0.009765625%

Output Analysis: chi_squared_distribution(1.0)
Typical Timing: 125 ± 12 ns
Statistics of 1024 samples:
 Minimum: 5.306492454827853e-09
 Median: (0.4420680734460275, 0.4441564689040373)
 Maximum: 11.56217687809815
 Mean: 0.9385607357356506
 Std Deviation: 1.3555135542655998
Post-processor distribution of 10240 samples using floor method:
 0: 68.505859375%
 1: 15.810546875%
 2: 7.666015625%
 3: 3.8671875%
 4: 1.69921875%
 5: 1.103515625%
 6: 0.60546875%
 7: 0.341796875%
 8: 0.107421875%
 9: 0.078125%
 10: 0.09765625%
 11: 0.048828125%
 12: 0.0390625%
 13: 0.01953125%
 19: 0.009765625%

Output Analysis: cauchy_distribution(0.0, 1.0)
Typical Timing: 63 ± 14 ns
Statistics of 1024 samples:
 Minimum: -498.4225750298302
 Median: (0.03433738724468461, 0.03670480336452593)
 Maximum: 123.33600380781016
 Mean: -0.6470505521541479
 Std Deviation: 20.104377568004953
Post-processor distribution of 10240 samples using floor_mod_10 method:
 0: 26.181640625%
 1: 11.7578125%
 2: 5.966796875%
 3: 3.798828125%
 4: 3.1640625%
 5: 3.33984375%
 6: 3.828125%
 7: 5.60546875%
 8: 10.830078125%
 9: 25.52734375%

Output Analysis: fisher_f_distribution(8.0, 8.0)
Typical Timing: 188 ± 15 ns
Statistics of 1024 samples:
 Minimum: 0.08633840628109077
 Median: (0.9810512057351255, 0.9846288796461584)
 Maximum: 34.86272012181962
 Mean: 1.3270992950089113
 Std Deviation: 1.5255073733976054
Post-processor distribution of 10240 samples using floor method:
 0: 50.60546875%
 1: 32.40234375%
 2: 10.341796875%
 3: 3.49609375%
 4: 1.54296875%
 5: 0.654296875%
 6: 0.341796875%
 7: 0.146484375%
 8: 0.185546875%
 9: 0.078125%
 10: 0.0390625%
 11: 0.029296875%
 13: 0.029296875%
 14: 0.009765625%
 15: 0.0390625%
 19: 0.009765625%
 24: 0.009765625%
 26: 0.009765625%
 27: 0.009765625%
 31: 0.009765625%
 34: 0.009765625%

Output Analysis: student_t_distribution(8.0)
Typical Timing: 125 ± 14 ns
Statistics of 1024 samples:
 Minimum: -5.648139405585209
 Median: (0.01642851297957229, 0.01764034375545864)
 Maximum: 4.937231407576627
 Mean: 0.0005738579894033376
 Std Deviation: 1.1201097183027962
Post-processor distribution of 10240 samples using round method:
 -6: 0.029296875%
 -5: 0.05859375%
 -4: 0.25390625%
 -3: 1.66015625%
 -2: 6.484375%
 -1: 22.87109375%
 0: 36.357421875%
 1: 23.583984375%
 2: 6.77734375%
 3: 1.591796875%
 4: 0.25390625%
 5: 0.05859375%
 6: 0.009765625%
 7: 0.009765625%


=========================================================================
Total Test Time: 0.5339 seconds