# Numbers sampled from exponential distribution seems to be incorrect

**URL:** <https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810>\
**Category:** Modelling & Simulations\
**Tags:** distributions\
**Created:** [May 10, 2022, 1:01pm UTC](https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810 "2022-05-10T13:01:58Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![efJerryYang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/efjerryyang/32/215784_2.png) [@efJerryYang](https://discourse.julialang.org/u/efJerryYang)\
**Post date:** [May 10, 2022, 1:01pm UTC](https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810/1 "2022-05-10T13:01:58Z")

</div>

I am running a simulation task which is supposed to sample data from an exponential distribution, but the results are always larger than correct ones. I converted my julia code to matlab and it produced correct results (without any logic and algorithm changes).

I checked my code until I found something weird similar to this, I wonder if this is a bug in `Distributions.jl`:

```julia
histogram(rand(Exponential(1e5),1000000),bins=256)

```

When running this line of code repeatedly in the REPL, I found that it displayed significantly 2 different histograms, and the incorrect one was clearer when I combined them into one plot (see below).

Both p (correct) and q (incorrect) are sampled this way and plotted using `histogram()`, and are 1000000-element vector:

```julia
julia> q = rand(Exponential(1e5),1000000) 

julia> histogram(q, bins=256, label="q") # after trying several times to find incorrect sample
...
julia> p = rand(Exponential(1e5),1000000)

julia> histogram!(p, bins=256, label="p")

```

 ![image](https://global.discourse-cdn.com/julialang/original/3X/c/6/c6917b8631b1479c338b4903e19b77d68294065a.png)

Both p and q are 1000000-element vector:

```julia
julia> q
1000000-element Vector{Float64}:
  36615.51140190222
      ⋮
  76827.76195613605

julia> p
1000000-element Vector{Float64}:
  95336.41621794412
      ⋮
 160348.4912588241

```

Here is the corresponding matlab code and result:

```matlab
>> histogram(exprnd(1e5,1000000,1),256)

```

 ![image](https://global.discourse-cdn.com/julialang/original/3X/9/0/903879358e4ad00a208c4bfafb8e366b539497b1.png)

It is worth noting that the `julia` sample results seem to be too “stable” compared to `matlab`. (I find it difficult to explain, but you might understand this after running such code both in julia and matlab. Anyway, this is not the core question I want to ask.)

julia version: `v1.7.2`  
package version: `Distributions.jl v0.25.58`

---

<div class="post-metadata">

**Author:** ![JM\_Beckers](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jm_beckers/32/22482_2.png) [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)\
**Post date:** [May 10, 2022, 1:18pm UTC](https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810/2 "2022-05-10T13:18:08Z")

</div>

> [@efJerryYang](#):
>
> `histogram(q, bins=256, label="q")`

I think the different shape is just due to different maximum values in the samples and therefore different bin sizes. Just try

```julia
q = rand(Exponential(1e5),1000000) 
histogram(q, bins=range(0.0, stop = 1.5E6, length = 256), label="q")

```

---

<div class="post-metadata">

**Author:** ![sylvaticus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sylvaticus/32/203883_2.png) [@sylvaticus](https://discourse.julialang.org/u/sylvaticus)\
**Post date:** [May 10, 2022, 1:18pm UTC](https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810/3 "2022-05-10T13:18:19Z")

</div>

> [@efJerryYang](#):
>
> ```julia
> q = rand(Exponential(1e5),1000000) 
> 
> julia> histogram(q, bins=256, label="q") # after trying several times to find incorrect sample
> ...
> julia> p = rand(Exponential(1e5),1000000)
> 
> julia> histogram!(p, bins=256, label="p")
> 
> ```

Can’t replicate.  
`p` and `q` look (plot) the same on my machine:

```julia

julia> using Distributions, Plots, Statistics

julia> q = rand(Exponential(1e5),1000000)
1000000-element Vector{Float64}:
  53746.7089587224
  25558.058373069543
  21390.660786270604
      ⋮
 194671.77955269578
   3261.280286248243

julia> histogram(q, bins=256, label="q") # after trying several times to find incorrect sample

julia> p = rand(Exponential(1e5),1000000)
1000000-element Vector{Float64}:
  86643.34310962744
  18451.649764193146
 229530.047033587
      ⋮
  39726.18702750079
  47451.27464180034

julia> histogram!(p, bins=256, label="p")

julia> mean(q)
99881.81845107871

julia> mean(p)
100103.12791672003

```

(@v1.7) pkg\> status  
Status `~/.julia/environments/v1.7/Project.toml`  
[024491cd] BetaML v0.6.0 `~/.julia/dev/BetaML`  
[a93c6f00] DataFrames v1.3.2  
[31c24e10] Distributions v0.25.58  
[e30172f5] Documenter v0.27.15 `~/.julia/dev/Documenter`  
[91a5bcdd] Plots v1.29.0  
[295af30f] Revise v3.3.3

---

<div class="post-metadata">

**Author:** ![efJerryYang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/efjerryyang/32/215784_2.png) [@efJerryYang](https://discourse.julialang.org/u/efJerryYang)\
**Post date:** [May 10, 2022, 1:39pm UTC](https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810/4 "2022-05-10T13:39:09Z")

</div>

Thank you, I understood.

---

<div class="post-metadata">

**Author:** ![efJerryYang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/efjerryyang/32/215784_2.png) [@efJerryYang](https://discourse.julialang.org/u/efJerryYang)\
**Post date:** [May 10, 2022, 1:40pm UTC](https://discourse.julialang.org/t/numbers-sampled-from-exponential-distribution-seems-to-be-incorrect/80810/5 "2022-05-10T13:40:22Z")

</div>

Thanks, I got the causes.