# non-normal
Generate a non-normal distributions with given a mean, variance, skewness and kurtosis using
the [Fleishman Method](https://link.springer.com/article/10.1007/BF02293811),
essentially a cubic transformation on a standard normal [X~N(0, 1)]
$$
Y =a +bX +cX^2 +dX^3
$$
where the coefficients ($a, b, c, d$) are tuned to create a distribution
with the desired statistic
Figure 1. A non-normal field generated in the `usage` section below. The title
shows the input parameters, and the emperically measured statistics of the
generated distribution
### Installation
Installs cleanly with a single invocation of the standard Python package tool:
```
$ pip install non-normal
```
### Usage
```
from non_normal import fleishman
# Input parameters for non-normal field
mean = 0
var = 1
skew = 1
ekurt = 2
size = 2**20
# Create an instance of the Fleishman class
ff = fleishman.Fleishman(mean=mean, var=var, skew=skew, ekurt=ekurt, size=size)
# Generate the field
ff.gen_field()
non_normal_data = ff.field
# Measure the stats of the generated samples
ff.field_stats
>>> {'mean': 0.000203128504124,
'var': 1.001352686678266,
'skew': 1.005612915524984,
'ekurt': 2.052527629375554,}
```
### References
1. [A method for simulating non-normal distributions](https://link.springer.com/article/10.1007/BF02293811)
2. [Functions for Simulating Data by Using Fleishman’s Transformation](https://support.sas.com/content/dam/SAS/support/en/books/simulating-data-with-sas/65378_Appendix_D_Functions_for_Simulating_Data_by_Using_Fleishmans_Transformation.pdf)
3. [Generation of Non-normal Data – A Study of Fleishman’s Power Method](https://www.diva-portal.org/smash/get/diva2:407995/FULLTEXT01.pd)
4. [Computing the real solutions of Fleishman's equations for simulating non-normal data](https://pubmed.ncbi.nlm.nih.gov/34779511/)
5. [Simulating multivariate nonnormal distributions](https://link.springer.com/article/10.1007/BF02293687)
6. [https://gist.github.com/zeimusu/7432603b85dc6406c6ea](https://gist.github.com/zeimusu/7432603b85dc6406c6ea)
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"description": "# non-normal\nGenerate a non-normal distributions with given a mean, variance, skewness and kurtosis using\nthe [Fleishman Method](https://link.springer.com/article/10.1007/BF02293811),\nessentially a cubic transformation on a standard normal [X~N(0, 1)]\n\n$$\nY =a +bX +cX^2 +dX^3\n$$\n\nwhere the coefficients ($a, b, c, d$) are tuned to create a distribution\nwith the desired statistic\n\n\nFigure 1. A non-normal field generated in the `usage` section below. The title\nshows the input parameters, and the emperically measured statistics of the \ngenerated distribution\n\n### Installation\n\nInstalls cleanly with a single invocation of the standard Python package tool:\n\n```\n$ pip install non-normal\n```\n\n### Usage\n\n```\nfrom non_normal import fleishman\n\n# Input parameters for non-normal field\nmean = 0\nvar = 1\nskew = 1\nekurt = 2\nsize = 2**20\n\n# Create an instance of the Fleishman class\nff = fleishman.Fleishman(mean=mean, var=var, skew=skew, ekurt=ekurt, size=size)\n\n# Generate the field\nff.gen_field()\nnon_normal_data = ff.field\n\n# Measure the stats of the generated samples\nff.field_stats\n\n>>> {'mean': 0.000203128504124, \n 'var': 1.001352686678266, \n 'skew': 1.005612915524984, \n 'ekurt': 2.052527629375554,}\n```\n\n### References\n\n1. [A method for simulating non-normal distributions](https://link.springer.com/article/10.1007/BF02293811)\n2. [Functions for Simulating Data by Using Fleishman\u2019s Transformation](https://support.sas.com/content/dam/SAS/support/en/books/simulating-data-with-sas/65378_Appendix_D_Functions_for_Simulating_Data_by_Using_Fleishmans_Transformation.pdf)\n3. [Generation of Non-normal Data \u2013 A Study of Fleishman\u2019s Power Method](https://www.diva-portal.org/smash/get/diva2:407995/FULLTEXT01.pd)\n4. [Computing the real solutions of Fleishman's equations for simulating non-normal data](https://pubmed.ncbi.nlm.nih.gov/34779511/)\n5. [Simulating multivariate nonnormal distributions](https://link.springer.com/article/10.1007/BF02293687)\n6. [https://gist.github.com/zeimusu/7432603b85dc6406c6ea](https://gist.github.com/zeimusu/7432603b85dc6406c6ea)\n",
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