Create series of random numbers fitting a specified distribution, and then analyze them.
Project description
Randalyze  Random Number Generator And Analyzer
What Does Randalyze Do?
Randalyze is a Python module that you can import or use directly from the command line to generate a set of random numbers. These numbers will fit a specified distribution, rather than just being evenly distributed.
It also allows you to analyze a set of numbers, to see which distribution they match.
At the moment, the only distribution that Randalyze handles is Benford's Law. It's a counterintuitive distribution that numbers from the real world tend to follow. So, if you want to see whether invoice totals, numbers of incidents, traffic counts, etc. are realistic, analyze them using Randalyze. Checking against Benford's Law is good enough for auditors, so there's definitely something to it!
Installation
Randalyze supports Python 3.8 and later, so you can install it on Windows 7 if you want. It doesn't support Python 2.7.
To install Randalyze, create a virtual environment and use pip
:
pip install randalyze
Usage
Command Line Usage
Generating Random Numbers
The generate
command creates a number of random numbers. The type of generator must be specified  currently the only option is benford
, and the number (or count) of numbers generated is specified with the c
option.
For example, to generate 100 random numbers with a Benford distribution, the following command line can be used:
randalyze generate c 100 benford
or, if you're not using an active virtual environment:
python m randalyze generate c 100 benford
For detailled parameter descriptions, use:
randalyze help
randalyze generate help
One parameter worth noting is a
, or adjustments
. Benford's Law applies when a quantity of individual numbers are combined, for example in a votes across a number of regions, an invoice, or a number of individuals infected with a disease on particular date. The value of the adjustments
parameter corresponds with how many numbers are combined to produce the final result. The higher this value, the more closely the generated numbers are likely to correspond to Benford's Law, but the longer it will take to generate the numbers. A lower number of adjustments will produce faster results, but they may not adhere as closely to Benford's Law.
Output Format
Randalyzer sends all of its output to stdout
, to allow the output to be piped to other processes. It can output the numbers it generates in any of the following formats:
Plain Text
This is an ideal format to pipe to other processes, including randalyze analyze
. Numbers are separated by a newline character, e.g.:
0.02983916017598411
0.013551386905062924
0.00024998215041082837
0.005491804395091004
0.02466273019653459
0.0063846564027225435
0.0016043375532727268
0.0026923403623502775
0.024469531291955015
0.003059618929054221
0.046573520246102486
0.0007443706751732054
6.522095130906779e06
0.03635226424464967
0.0013066769632407483
0.008161073155635998
0.0382949028445558
0.007312698653941686
0.0028210034630940573
0.022493548691029038
You can also use the w
/ wholedigits
and d
/ fractiondigits
to specify the maximum number of digit in the whole and fraction part of the numbers respectively. For example:
randalyze generate benford c 10 w 7 d 2
will output a list of 10 numbers, with a maximum of 7 digits before the decimal point and 2 afterwards, e.g.:
20199.5
207302.05
183079.86
307597.46
1516574.65
1029.38
1442196.64
374390.6
91128.55
33184.82
JSON
If you're passing the data around between processes and straightforward piping is not the answer, JSON format can be produced instead:
[0.021875574255089396,0.01363138644672022,0.04880603372115697,0.00044507604221987146,0.0276700261238657,0.03214714230191736,0.02915457360778051,0.04708394499413024,0.0001520800546499388,0.0008435362137085937,0.008981908758960934,0.025213372748772594,0.2523350721739971,0.001618197247836204,0.009578408659261814,0.02682977173023309,0.043980297143841836,0.010087407530137727,0.022770430657528977,0.007422951888962673]
CSV
If you want to import the generated data into a process that requires CSV data, generate it in CSV format:
numbers,
0.046614057519653466,
0.03791869719865344,
0.0384657633546525,
2.855767617145996e05,
0.01146753335163042,
0.03691158797807547,
0.003926152675269877,
0.05987977588577215,
0.03282925392769393,
0.03005755057310207,
2.597019093156996e05,
0.009355992571839502,
9.107989223269995e05,
0.0025864757492692577,
0.0008046680877702718,
0.003676954411104498,
0.0023820723499611567,
0.004461646162414915,
0.012232037104772345,
0.08673320229596392
Analyzing Numbers
If you have a set of numbers, randalyze
can analyze them and tell you how close to a Benford distribution they are. These numbers may have been generated by randalyze
, or maybe obtained from somewhere else  it really doesn't matter.
So, to analyze an output of 10,000 numbers from the randalyze generate
command, and see whether it matches a Benford distribution to within 10%, use:
randalyze generate benford c 10000  randalyze analyze t 10 benford
And to ensure the numbers in a text file numbers.txt
, with one number per line, fit a Benford distribution:
cat numbers.txt  randalyze analyze t 10 benford
or use the FILE
parameter:
randalyze analyze t 10 benford numbers.txt
And to produce the output in JSON format:
randalyze analyze t 10 format json benford numbers.txt
Ouput Format
Like its generated data, Randalyzer sends all of its analysis details to stdout
. You can choose from a couple of formats:
Text Format
Plain text format analyses are in the following format:
Benford Analysis Result
First Digits Expected vs Actual:
1 3010 : 3139 > 4.3%
2 1760 : 1755 > 0.3%
3 1249 : 1220 > 2.4%
4 969 : 912 > 5.9%
5 791 : 773 > 2.4%
6 669 : 650 > 2.9%
7 579 : 613 > 5.7%
8 511 : 504 > 1.5%
9 457 : 434 > 5.2%
Maximum difference: 5.9%
Benford (tolerance 10.0%)? True
The expected digit count is calculated from Benford's law and rounded to the nearest integer. The actual number of occurences of the digit is in the next column, and the percentage difference between the two is in the last column.
JSON
Randalyze's analyser JSON output is in the following format:
{
"distributions": [
{
"name": "benford",
"matches": true,
"first_digit": {
"distribution": {
"0": 0.0,
"1": 0.30246,
"2": 0.17439,
"3": 0.12504,
"4": 0.09564,
"5": 0.07993,
"6": 0.06695,
"7": 0.05743,
"8": 0.05178,
"9": 0.04638
},
"counts": {
"0": 0,
"1": 30246,
"2": 17439,
"3": 12504,
"4": 9564,
"5": 7993,
"6": 6695,
"7": 5743,
"8": 5178,
"9": 4638
}
}
}
]
}
The distribution
dictionary contains the fraction of the total numbers that started with each digit. The counts
dictionary contains the count of each number that started with each digit.
Self Testing
You can use randalyze
to analyze the numbers it creates by piping the output of the generate
command into the analyze
command. For example, to check whether 10,000 generated numbers are wihin 10% of a Benford distribution, use:
randalyze generate benford c 10000  randalyze analyze t 10 benford
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