# Random number generation from a power law
**URL:** https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701
**Category:** General Usage
**Tags:** question, package
**Created:** [June 22, 2023, 1:11pm UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701 "2023-06-22T13:11:34Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@ABCD](https://discourse.julialang.org/u/ABCD)
#### Post date: [June 22, 2023, 1:11pm UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/1 "2023-06-22T13:11:34Z")
hello all,
I am new to Julia. I need to generate random numbers from power law, broken power law and different distributions. Is there a package that do all of these? Thank you very much in advance.
---
### Author:  [@frylock](https://discourse.julialang.org/u/frylock)
#### Post date: [June 22, 2023, 2:56pm UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/2 "2023-06-22T14:56:43Z")
Welcome to the discussion board. 🙂
I have not used this, but perhaps [Distributions.jl](https://juliastats.org/Distributions.jl/stable/) might work for you?
---
### Author:  [@empet](https://discourse.julialang.org/u/empet)
#### Post date: [June 22, 2023, 6:29pm UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/3 "2023-06-22T18:29:55Z")
More precisely, here [https://juliastats.org/Distributions.jl/stable/univariate/#Sampling-(Random-number-generation)](https://juliastats.org/Distributions.jl/stable/univariate/#Sampling-(Random-number-generation)) you can find the univariate distributions and sampling from an arbitrary one.
Example:
```julia
using Distributions, Plots
plotlyjs()
const α = 2.75
const xmin= 3.0
d = Pareto(α, xmin)
smpl= rand(d, 1000)
h=histogram(smpl, bins= xmin:50, normalize=:pdf,
framestyle=:box, size=(500, 250), legend=false)
```
Broken power law distribution is not implemented in Distributions.jl. It depends on the number of break points and power indices on each interval.
I only know of the existence of the broken power law, implemented in astropy: [https://docs.astropy.org/en/stable/\_modules/astropy/modeling/powerlaws.html](https://docs.astropy.org/en/stable/_modules/astropy/modeling/powerlaws.html), but without a sampling method.
---
### Author:  [@bertschi](https://discourse.julialang.org/u/bertschi)
#### Post date: [June 22, 2023, 8:49pm UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/4 "2023-06-22T20:49:52Z")
Don’t know much about broken power laws, but mixture models might be able to piece them together:
```julia
alpha_below = 1.6
alpha_above = 1.2
breakpoint = 5.4
p_below = cdf(Pareto(alpha_below), breakpoint)
broken_dist = MixtureModel([truncated(Pareto(alpha_below), nothing, breakpoint),
truncated(Pareto(alpha_above), breakpoint, nothing)],
[p_below, 1 - p_below])
rand(broken_dist)
```
---
### Author:  [@cmarcotte](https://discourse.julialang.org/u/cmarcotte)
#### Post date: [June 23, 2023, 8:30am UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/5 "2023-06-23T08:30:04Z")
If your distribution is known and sufficiently smooth\[1\] you can use [ApproxFun.jl](https://juliaapproximation.github.io/ApproxFun.jl/latest/generated/Sampling/).
* * *
1. Though in practice 2M Chebyshev modes is enough to approximate some very wonky functions.
---
### Author:  [@cgarling](https://discourse.julialang.org/u/cgarling)
#### Post date: [June 27, 2023, 10:53am UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/6 "2023-06-27T10:53:12Z")
I implemented broken-power-law sampling in [InitialMassFunctions.jl](https://github.com/cgarling/InitialMassFunctions.jl), which is now a registered package. This functionality is provided by the `BrokenPowerLaw` type. This type implements the Distributions.jl [`sampler` API](https://juliastats.org/Distributions.jl/stable/extends/#Distributions.sampler-Tuple%7BDistribution%7D), so a more efficient object for sampling can be constructed via `Distributions.sampler(::BrokenPowerLaw)`. You may also be interested in the single power-law `PowerLawIMF` type, which is just a wrapper on top of the Pareto distribution from [Distributions.jl](https://juliastats.org/Distributions.jl/stable/univariate/#Distributions.Pareto).
---
### Author:  [@ABCD](https://discourse.julialang.org/u/ABCD)
#### Post date: [July 16, 2023, 7:09am UTC](https://discourse.julialang.org/t/random-number-generation-from-a-power-law/100701/7 "2023-07-16T07:09:15Z")
All of this is really helpful. Thanks a lot!