{
    "info": {
        "author": "Robert Sharp",
        "author_email": "webmaster@sharpdesigndigital.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 5 - Production/Stable",
            "Operating System :: MacOS :: MacOS X",
            "Operating System :: POSIX :: Linux",
            "Programming Language :: C++",
            "Programming Language :: Cython",
            "Programming Language :: Python :: 3.6",
            "Topic :: Software Development :: Libraries :: Python Modules"
        ],
        "description": "# Random Number Generator & Engine for Python3\n- Compiled Python3 API for the C++ Random Library.\n- Designed for python developers familiar with C++ random library.\n- Warning: RNG is not suitable for cryptography or secure hashing.\n\n\n### Quick Install `$ pip install RNG`\n\n\n### Installation may require the following:\n- Python 3.6 or later with dev tools (setuptools, pip, etc.)\n- Cython: Bridge from C/C++ to Python.\n- Modern C++17 Compiler and Standard Library.\n\n\n### Sister Projects:\n- Fortuna: Collection of tools to make custom random value generators. https://pypi.org/project/Fortuna/\n- Pyewacket: Drop-in replacement for the Python3 random module. https://pypi.org/project/Pyewacket/\n- MonkeyScope: Framework for testing non-deterministic generators. https://pypi.org/project/MonkeyScope/\n\n\n---\n\n## RNG Specifications\n\n#### Random Boolean\n- `RNG.bernoulli_variate(ratio_of_truth: float) -> bool`\n    - Produces a Bernoulli distribution of boolean values.\n    - @param ratio_of_truth :: the probability of True. Expected input range: `[0.0, 1.0]`, clamped.\n    - @return :: True or False\n\n\n#### Random Integer\n- `RNG.uniform_int_variate(left_limit: int, right_limit: int) -> int`\n    - Flat uniform distribution.\n    - @param left_limit :: input A.\n    - @param right_limit :: input B. \n    - @return :: random integer in the inclusive range `[A, B]` or `[B, A]` if B < A\n- `RNG.binomial_variate(number_of_trials: int, probability: float) -> int`\n    - Based on the idea of flipping a coin and counting how many heads come up after some number of flips.\n    - @param number_of_trials :: how many times to flip a coin.\n    - @param probability :: how likely heads will be flipped. 0.5 is a fair coin. 1.0 is a double headed coin.\n    - @return :: count of how many heads came up.\n- `RNG.negative_binomial_variate(trial_successes: int, probability: float) -> int`\n    - Based on the idea of flipping a coin as long as it takes to succeed.\n    - @param trial_successes :: the required number of heads flipped to succeed.\n    - @param probability :: how likely heads will be flipped. 0.50 is a fair coin.\n    - @return :: the count of how many tails came up before the required number of heads.\n- `RNG.geometric_variate(probability: float) -> int`\n    - Same as random_negative_binomial(1, probability). \n- `RNG.poisson_variate(mean: float) -> int`\n    - @param mean :: sets the average output of the function.\n    - @return :: random integer, poisson distribution centered on the mean.\n\n\n#### Random Floating Point\n- `RNG.generate_canonical() -> float`\n    - Evenly distributes floats of maximum precision.\n    - @return :: random float in range (0.0, 1.0)\n- `RNG.uniform_real_variate(left_limit: float, right_limit: float) -> float`\n    - Flat uniform distribution of floats.\n    - @return :: random Float between left_limit and right_limit.\n- `RNG.normal_variate(mean: float, std_dev: float) -> float`\n    - @param mean :: sets the average output of the function.\n    - @param std_dev :: standard deviation. Specifies spread of data from the mean.\n- `RNG.lognormal_variate(log_mean: float, log_deviation: float) -> float`\n    - @param log_mean :: sets the log of the mean of the function.\n    - @param log_deviation :: log of the standard deviation. Specifies spread of data from the mean.\n- `RNG.exponential_variate(lambda_rate: float) -> float`\n    - Produces random non-negative floating-point values, distributed according to probability density function.\n    - @param lambda_rate :: \u03bb constant rate of a random event per unit of time/distance.\n    - @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.\n- `RNG.gamma_variate(shape: float, scale: float) -> float`\n    - Generalization of the exponential distribution.\n    - Produces random positive floating-point values, distributed according to probability density function.    \n    - @param shape :: \u03b1 the number of independent exponentially distributed random variables.\n    - @param scale :: \u03b2 the scale factor or the mean of each of the distributed random variables.\n    - @return :: the sum of \u03b1 independent exponentially distributed random variables, each of which has a mean of \u03b2.\n- `RNG.weibull_variate(shape: float, scale: float) -> float`\n    - Generalization of the exponential distribution.\n    - Similar to the gamma distribution but uses a closed form distribution function.\n    - Popular in reliability and survival analysis.\n- `RNG.extreme_value_variate(location: float, scale: float) -> float`\n    - Based on Extreme Value Theory. \n    - Used for statistical models of the magnitude of earthquakes and volcanoes.\n- `RNG.chi_squared_variate(degrees_of_freedom: float) -> float`\n    - Used with the Chi Squared Test and Null Hypotheses to test if sample data fits an expected distribution.\n- `RNG.cauchy_variate(location: float, scale: float) -> float`\n    - @param location :: It specifies the location of the peak. The default value is 0.0.\n    - @param scale :: It represents the half-width at half-maximum. The default value is 1.0.\n    - @return :: Continuous Distribution.\n- `RNG.fisher_f_variate(degrees_of_freedom_1: float, degrees_of_freedom_2: float) -> float`\n    - F distributions often arise when comparing ratios of variances.\n- `RNG.student_t_variate(degrees_of_freedom: float) -> float`\n    - T distribution. Same as a normal distribution except it uses the sample standard deviation rather than the population standard deviation.\n    - As degrees_of_freedom goes to infinity it converges with the normal distribution.\n\n\n## Development Log\n##### RNG 1.6.6\n- Documentation Update\n\n##### RNG 1.6.5\n- Fixed Typos\n\n##### RNG 1.6.4\n- Installer update.\n\n##### RNG 1.6.3\n- More minor typos fixed.\n\n##### RNG 1.6.2\n- Minor typos fixed.\n\n##### RNG 1.6.1\n- Storm 3.2.2 Update.\n\n##### RNG 1.6.0\n- RNG is now compatible with python notebooks.\n\n##### RNG 1.5.5\n- Storm Update\n\n##### RNG 1.5.4\n- Storm 3.2 Update\n\n##### RNG 1.5.3\n- Fixed Typos\n\n##### RNG 1.5.2\n- Compiler Config Update\n\n##### RNG 1.5.1\n- A number of testing routines have been extracted into a new module: MonkeyScope.\n    - distribution\n    - timer\n    - distribution_timer\n\n##### RNG 1.5.0, internal\n- Further API Refinements, new naming convention for variate generators: `<algorithm name>_variate`\n\n##### RNG 1.4.2\n- Install script update\n- Test tweaks for noise reduction in timing tests.\n\n##### RNG 1.4.1\n- Test Patch for new API\n- Documentation Updates\n\n##### RNG 1.4.0\n- API Refactoring\n\n##### RNG 1.3.4\n- Storm Update 3.1.1\n\n##### RNG 1.3.3\n- Installer script update\n\n##### RNG 1.3.2\n- Minor Bug Fix\n\n##### RNG 1.3.1\n- Test Update\n\n##### RNG 1.3.1\n- Fixed Typos\n\n##### RNG 1.3.0\n- Storm Update\n\n##### RNG 1.2.5\n- Low level clean up\n\n##### RNG 1.2.4\n- Minor Typos Fixed\n\n##### RNG 1.2.3\n- Documentation Update\n- Test Update\n- Bug Fixes\n\n##### RNG 1.0.0 - 1.2.2, internal\n- API Changes:\n    - randint changed to random_int\n    - randbelow changed to random_below\n    - random changed to generate_canonical\n    - uniform changed to random_float\n\n##### RNG 0.2.3\n- Bug Fixes\n\n##### RNG 0.2.2\n- discrete() removed.\n\n##### RNG 0.2.1\n- minor typos\n- discrete() depreciated.\n\n##### RNG 0.2.0\n- Major Rebuild.\n\n##### RNG 0.1.22\n- The RNG Storm Engine is now the default standard.\n- Experimental Vortex Engine added for testing.\n\n##### RNG 0.1.21 beta\n- Small update to the testing suite.\n\n##### RNG 0.1.20 beta\n- Changed default inputs for random_int and random_below to sane values.\n    - random_int(left_limit=1, right_limit=20) down from `-2**63, 2**63 - 1`\n    - random_below(upper_bound=10) down from `2**63 - 1`\n\n##### RNG 0.1.19 beta\n- Broke some fixed typos, for a change of pace.\n\n##### RNG 0.1.18 beta\n- Fixed some typos.\n\n##### RNG 0.1.17 beta\n- Major Refactoring.\n- New primary engine: Hurricane.\n- Experimental engine Typhoon added: random_below() only.\n\n##### RNG 0.1.16 beta\n- Internal Engine Performance Tuning. \n\n##### RNG 0.1.15 beta\n- Engine Testing.\n\n##### RNG 0.1.14 beta\n- Fixed a few typos.\n\n##### RNG 0.1.13 beta\n- Fixed a few typos.\n\n##### RNG 0.1.12 beta\n- Major Test Suite Upgrade.\n- Major Bug Fixes.\n    - Removed several 'foot-guns' in prep for fuzz testing in future releases.\n\n##### RNG 0.1.11 beta\n- Fixed small bug in the install script.\n\n##### RNG 0.1.10 beta\n- Fixed some typos.\n\n##### RNG 0.1.9 beta\n- Fixed some typos.\n\n##### RNG 0.1.8 beta\n- Fixed some typos.\n- More documentation added.\n\n##### RNG 0.1.7 beta\n- The `random_floating_point` function renamed to `random_float`.\n- The function `c_rand()` has been removed as well as all the cruft it required.\n- Major Documentation Upgrade.\n- Fixed an issue where keyword arguments would fail to propagate. Both, positional args and kwargs now work as intended.\n- Added this Dev Log.\n\n##### RNG 0.0.6 alpha\n- Minor ABI changes.\n\n##### RNG 0.0.5 alpha\n- Tests redesigned slightly for Float functions.\n\n##### RNG 0.0.4 alpha\n- Random Float Functions Implemented.\n\n##### RNG 0.0.3 alpha\n- Random Integer Functions Implemented.\n\n##### RNG 0.0.2 alpha\n- Random Bool Function Implemented.\n\n##### RNG 0.0.1 pre-alpha\n- Planning & Design.\n\n\n## MonkeyScope: Distribution and Performance Test Suite\n```\nMonkeyScope: RNG Tests\n=========================================================================\n\nBoolean Variate Distributions\n\nOutput Analysis: bernoulli_variate(0.0)\nTypical Timing: 36 \u00b1 5 ns\nStatistics of 1000 samples:\n Minimum: False\n Median: False\n Maximum: False\n Mean: 0.0\n Std Deviation: 0.0\nDistribution of 10000 samples:\n False: 100.0%\n\nOutput Analysis: bernoulli_variate(0.3333333333333333)\nTypical Timing: 41 \u00b1 7 ns\nStatistics of 1000 samples:\n Minimum: False\n Median: False\n Maximum: True\n Mean: 0.314\n Std Deviation: 0.46411636471902173\nDistribution of 10000 samples:\n False: 66.93%\n True: 33.07%\n\nOutput Analysis: bernoulli_variate(0.5)\nTypical Timing: 40 \u00b1 5 ns\nStatistics of 1000 samples:\n Minimum: False\n Median: False\n Maximum: True\n Mean: 0.494\n Std Deviation: 0.4999639987039066\nDistribution of 10000 samples:\n False: 50.59%\n True: 49.41%\n\nOutput Analysis: bernoulli_variate(0.6666666666666666)\nTypical Timing: 40 \u00b1 5 ns\nStatistics of 1000 samples:\n Minimum: False\n Median: True\n Maximum: True\n Mean: 0.684\n Std Deviation: 0.46491289506745237\nDistribution of 10000 samples:\n False: 33.22%\n True: 66.78%\n\nOutput Analysis: bernoulli_variate(1.0)\nTypical Timing: 32 \u00b1 1 ns\nStatistics of 1000 samples:\n Minimum: True\n Median: True\n Maximum: True\n Mean: 1.0\n Std Deviation: 0.0\nDistribution of 10000 samples:\n True: 100.0%\n\n\nInteger Variate Distributions\n\nBase Case\nOutput Analysis: Random.randint(1, 6)\nTypical Timing: 1088 \u00b1 61 ns\nStatistics of 1000 samples:\n Minimum: 1\n Median: 4\n Maximum: 6\n Mean: 3.532\n Std Deviation: 1.6914419883637746\nDistribution of 10000 samples:\n 1: 16.79%\n 2: 16.93%\n 3: 16.16%\n 4: 16.82%\n 5: 16.18%\n 6: 17.12%\n\nOutput Analysis: uniform_int_variate(1, 6)\nTypical Timing: 59 \u00b1 8 ns\nStatistics of 1000 samples:\n Minimum: 1\n Median: 3\n Maximum: 6\n Mean: 3.426\n Std Deviation: 1.7408400271133475\nDistribution of 10000 samples:\n 1: 17.01%\n 2: 16.39%\n 3: 16.66%\n 4: 16.5%\n 5: 16.71%\n 6: 16.73%\n\nOutput Analysis: binomial_variate(4, 0.5)\nTypical Timing: 140 \u00b1 13 ns\nStatistics of 1000 samples:\n Minimum: 0\n Median: 2\n Maximum: 4\n Mean: 2.038\n Std Deviation: 0.984152427218467\nDistribution of 10000 samples:\n 0: 6.12%\n 1: 25.1%\n 2: 37.29%\n 3: 25.0%\n 4: 6.49%\n\nOutput Analysis: negative_binomial_variate(5, 0.75)\nTypical Timing: 118 \u00b1 6 ns\nStatistics of 1000 samples:\n Minimum: 0\n Median: 1\n Maximum: 8\n Mean: 1.685\n Std Deviation: 1.4885479501850116\nDistribution of 10000 samples:\n 0: 23.35%\n 1: 29.92%\n 2: 22.14%\n 3: 12.89%\n 4: 6.53%\n 5: 2.98%\n 6: 1.4%\n 7: 0.49%\n 8: 0.17%\n 9: 0.06%\n 10: 0.02%\n 11: 0.04%\n 13: 0.01%\n\nOutput Analysis: geometric_variate(0.75)\nTypical Timing: 47 \u00b1 4 ns\nStatistics of 1000 samples:\n Minimum: 0\n Median: 0\n Maximum: 5\n Mean: 0.316\n Std Deviation: 0.6404248589803491\nDistribution of 10000 samples:\n 0: 75.33%\n 1: 18.4%\n 2: 4.72%\n 3: 1.12%\n 4: 0.34%\n 5: 0.07%\n 6: 0.01%\n 7: 0.01%\n\nOutput Analysis: poisson_variate(4.5)\nTypical Timing: 110 \u00b1 6 ns\nStatistics of 1000 samples:\n Minimum: 0\n Median: 4\n Maximum: 12\n Mean: 4.454\n Std Deviation: 2.1042537869753257\nDistribution of 10000 samples:\n 0: 1.16%\n 1: 5.0%\n 2: 11.72%\n 3: 16.76%\n 4: 18.74%\n 5: 17.24%\n 6: 12.49%\n 7: 8.34%\n 8: 4.72%\n 9: 2.38%\n 10: 0.83%\n 11: 0.41%\n 12: 0.14%\n 13: 0.05%\n 14: 0.02%\n\n\nFloating Point Variate Distributions\n\nBase Case\nOutput Analysis: Random.random()\nTypical Timing: 32 \u00b1 1 ns\nStatistics of 1000 samples:\n Minimum: 0.00020470717953002815\n Median: (0.4902766190643588, 0.49287975190577293)\n Maximum: 0.9998379746872317\n Mean: 0.4932275568514134\n Std Deviation: 0.2943772077006881\nPost-processor distribution of 10000 samples using round method:\n 0: 50.0%\n 1: 50.0%\n\nOutput Analysis: generate_canonical()\nTypical Timing: 38 \u00b1 4 ns\nStatistics of 1000 samples:\n Minimum: 0.0018313969488656262\n Median: (0.4999019745098515, 0.5000103956471701)\n Maximum: 0.9979157465022215\n Mean: 0.4983743559000373\n Std Deviation: 0.2857287394134513\nPost-processor distribution of 10000 samples using round method:\n 0: 50.0%\n 1: 50.0%\n\nBase Case\nOutput Analysis: Random.uniform(0.0, 10.0)\nTypical Timing: 229 \u00b1 16 ns\nStatistics of 1000 samples:\n Minimum: 0.0011475989233244999\n Median: (4.686759881204559, 4.698175014514612)\n Maximum: 9.994578954522886\n Mean: 4.90558557056895\n Std Deviation: 2.8901372998841577\nPost-processor distribution of 10000 samples using floor method:\n 0: 9.58%\n 1: 10.5%\n 2: 10.06%\n 3: 10.09%\n 4: 10.19%\n 5: 9.98%\n 6: 10.21%\n 7: 9.76%\n 8: 10.05%\n 9: 9.58%\n\nOutput Analysis: uniform_real_variate(0.0, 10.0)\nTypical Timing: 41 \u00b1 7 ns\nStatistics of 1000 samples:\n Minimum: 0.003871772166954936\n Median: (4.975709613518741, 4.99955707001919)\n Maximum: 9.99847163973721\n Mean: 5.041222981691081\n Std Deviation: 2.8720806186652457\nPost-processor distribution of 10000 samples using floor method:\n 0: 10.33%\n 1: 9.62%\n 2: 10.08%\n 3: 10.11%\n 4: 9.57%\n 5: 10.12%\n 6: 9.88%\n 7: 9.97%\n 8: 10.53%\n 9: 9.79%\n\nBase Case\nOutput Analysis: Random.expovariate(1.0)\nTypical Timing: 336 \u00b1 21 ns\nStatistics of 1000 samples:\n Minimum: 0.0008104371505790905\n Median: (0.6999357838616548, 0.7018251058756864)\n Maximum: 7.266089757629259\n Mean: 1.0321635246736387\n Std Deviation: 1.084028320793121\nPost-processor distribution of 10000 samples using floor method:\n 0: 63.7%\n 1: 22.72%\n 2: 8.33%\n 3: 3.3%\n 4: 1.26%\n 5: 0.4%\n 6: 0.22%\n 7: 0.04%\n 8: 0.01%\n 9: 0.01%\n 11: 0.01%\n\nOutput Analysis: exponential_variate(1.0)\nTypical Timing: 58 \u00b1 8 ns\nStatistics of 1000 samples:\n Minimum: 0.00018170037869458518\n Median: (0.7377113850720796, 0.7382275278647656)\n Maximum: 7.084870250885541\n Mean: 1.0149957923408772\n Std Deviation: 0.9661594059665878\nPost-processor distribution of 10000 samples using floor method:\n 0: 63.61%\n 1: 23.32%\n 2: 8.32%\n 3: 3.09%\n 4: 1.22%\n 5: 0.26%\n 6: 0.07%\n 7: 0.09%\n 8: 0.01%\n 10: 0.01%\n\nBase Case\nOutput Analysis: Random.gammavariate(1.0, 1.0)\nTypical Timing: 487 \u00b1 38 ns\nStatistics of 1000 samples:\n Minimum: 0.0010269090045949092\n Median: (0.6758922146292059, 0.6764364701429871)\n Maximum: 6.62473131254665\n Mean: 0.9526441065384418\n Std Deviation: 0.9235697791084873\nPost-processor distribution of 10000 samples using floor method:\n 0: 62.38%\n 1: 23.78%\n 2: 8.78%\n 3: 3.13%\n 4: 1.15%\n 5: 0.51%\n 6: 0.15%\n 7: 0.08%\n 8: 0.03%\n 9: 0.01%\n\nOutput Analysis: gamma_variate(1.0, 1.0)\nTypical Timing: 59 \u00b1 6 ns\nStatistics of 1000 samples:\n Minimum: 7.943300227810338e-05\n Median: (0.7410362381108585, 0.7486551841969276)\n Maximum: 9.45441577468242\n Mean: 1.0319939318688074\n Std Deviation: 1.0133677265428946\nPost-processor distribution of 10000 samples using floor method:\n 0: 63.46%\n 1: 23.11%\n 2: 8.67%\n 3: 3.01%\n 4: 1.18%\n 5: 0.37%\n 6: 0.08%\n 7: 0.07%\n 8: 0.03%\n 9: 0.02%\n\nBase Case\nOutput Analysis: Random.weibullvariate(1.0, 1.0)\nTypical Timing: 429 \u00b1 28 ns\nStatistics of 1000 samples:\n Minimum: 0.00014457030695612128\n Median: (0.6976139576861516, 0.6988385606862981)\n Maximum: 7.441929633011179\n Mean: 1.0360647371223919\n Std Deviation: 1.0423724124307105\nPost-processor distribution of 10000 samples using floor method:\n 0: 62.26%\n 1: 23.95%\n 2: 8.67%\n 3: 3.29%\n 4: 1.1%\n 5: 0.43%\n 6: 0.17%\n 7: 0.08%\n 8: 0.03%\n 9: 0.02%\n\nOutput Analysis: weibull_variate(1.0, 1.0)\nTypical Timing: 97 \u00b1 11 ns\nStatistics of 1000 samples:\n Minimum: 0.0001784696086844487\n Median: (0.6941698928066924, 0.6948215528368951)\n Maximum: 8.369567364716502\n Mean: 0.9966718438000562\n Std Deviation: 0.9674836941611771\nPost-processor distribution of 10000 samples using floor method:\n 0: 63.68%\n 1: 23.0%\n 2: 8.41%\n 3: 3.08%\n 4: 1.33%\n 5: 0.28%\n 6: 0.16%\n 7: 0.03%\n 8: 0.03%\n\nOutput Analysis: extreme_value_variate(0.0, 1.0)\nTypical Timing: 79 \u00b1 9 ns\nStatistics of 1000 samples:\n Minimum: -2.0871331458605598\n Median: (0.3869710970824426, 0.3904990435365016)\n Maximum: 6.870642194863319\n Mean: 0.5738754165001632\n Std Deviation: 1.2729399422463183\nPost-processor distribution of 10000 samples using round method:\n -2: 1.2%\n -1: 18.28%\n 0: 35.12%\n 1: 26.2%\n 2: 11.5%\n 3: 4.59%\n 4: 2.04%\n 5: 0.62%\n 6: 0.24%\n 7: 0.11%\n 8: 0.07%\n 9: 0.03%\n\nBase Case\nOutput Analysis: Random.gauss(5.0, 2.0)\nTypical Timing: 579 \u00b1 4 ns\nStatistics of 1000 samples:\n Minimum: -1.0864435352344746\n Median: (4.896021009703201, 4.8960635966136605)\n Maximum: 11.016252215240552\n Mean: 4.965365989325721\n Std Deviation: 1.9758300884950102\nPost-processor distribution of 10000 samples using round method:\n -2: 0.04%\n -1: 0.21%\n 0: 0.82%\n 1: 2.82%\n 2: 6.33%\n 3: 11.97%\n 4: 17.45%\n 5: 19.95%\n 6: 17.63%\n 7: 12.03%\n 8: 6.67%\n 9: 2.89%\n 10: 0.96%\n 11: 0.21%\n 12: 0.02%\n\nOutput Analysis: normal_variate(5.0, 2.0)\nTypical Timing: 87 \u00b1 2 ns\nStatistics of 1000 samples:\n Minimum: -2.405912295794069\n Median: (5.0738045445174995, 5.082279716366891)\n Maximum: 12.381509481018478\n Mean: 5.092836336120188\n Std Deviation: 2.014023813195181\nPost-processor distribution of 10000 samples using round method:\n -2: 0.06%\n -1: 0.28%\n 0: 0.79%\n 1: 2.77%\n 2: 6.21%\n 3: 12.0%\n 4: 17.38%\n 5: 19.86%\n 6: 17.04%\n 7: 13.02%\n 8: 6.47%\n 9: 3.01%\n 10: 0.83%\n 11: 0.22%\n 12: 0.05%\n 13: 0.01%\n\nBase Case\nOutput Analysis: Random.lognormvariate(1.6, 0.25)\nTypical Timing: 871 \u00b1 28 ns\nStatistics of 1000 samples:\n Minimum: 2.1400232821020095\n Median: (4.970649274737473, 4.972897691731108)\n Maximum: 11.584234487161941\n Mean: 5.099080347282304\n Std Deviation: 1.2828682146566066\nPost-processor distribution of 10000 samples using round method:\n 2: 0.35%\n 3: 7.51%\n 4: 27.79%\n 5: 30.41%\n 6: 19.95%\n 7: 9.09%\n 8: 3.4%\n 9: 0.96%\n 10: 0.43%\n 11: 0.07%\n 12: 0.03%\n 14: 0.01%\n\nOutput Analysis: lognormal_variate(1.6, 0.25)\nTypical Timing: 111 \u00b1 10 ns\nStatistics of 1000 samples:\n Minimum: 2.0565509130084196\n Median: (4.951319938162054, 4.956358747365627)\n Maximum: 10.705411301927128\n Mean: 5.084514398741803\n Std Deviation: 1.2702879123571864\nPost-processor distribution of 10000 samples using round method:\n 2: 0.23%\n 3: 7.93%\n 4: 26.34%\n 5: 31.23%\n 6: 20.45%\n 7: 9.02%\n 8: 3.25%\n 9: 1.12%\n 10: 0.33%\n 11: 0.08%\n 12: 0.02%\n\nOutput Analysis: chi_squared_variate(1.0)\nTypical Timing: 123 \u00b1 14 ns\nStatistics of 1000 samples:\n Minimum: 4.560050044340425e-07\n Median: (0.43843953531720004, 0.44248536881992023)\n Maximum: 12.827094790848676\n Mean: 1.0076909905738598\n Std Deviation: 1.4661644618564504\nPost-processor distribution of 10000 samples using floor method:\n 0: 68.66%\n 1: 15.68%\n 2: 7.28%\n 3: 3.75%\n 4: 2.04%\n 5: 1.08%\n 6: 0.69%\n 7: 0.35%\n 8: 0.2%\n 9: 0.09%\n 10: 0.1%\n 11: 0.02%\n 12: 0.03%\n 13: 0.01%\n 15: 0.02%\n\nOutput Analysis: cauchy_variate(0.0, 1.0)\nTypical Timing: 81 \u00b1 7 ns\nStatistics of 1000 samples:\n Minimum: -80.60257833512122\n Median: (-0.07136445696912773, -0.06912576811779096)\n Maximum: 302.9285259983777\n Mean: 0.048158350818380484\n Std Deviation: 14.33030682036316\nPost-processor distribution of 10000 samples using floor_mod_10 method:\n 0: 25.9%\n 1: 11.52%\n 2: 5.6%\n 3: 3.76%\n 4: 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