# Multivariate empirical characteristic function

**URL:** <https://discourse.julialang.org/t/multivariate-empirical-characteristic-function/63311>\
**Category:** Statistics\
**Created:** [June 21, 2021, 4:21pm UTC](https://discourse.julialang.org/t/multivariate-empirical-characteristic-function/63311 "2021-06-21T16:21:11Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Neurosurg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/neurosurg/32/26324_2.png) [@Neurosurg](https://discourse.julialang.org/u/Neurosurg)\
**Post date:** [June 21, 2021, 4:21pm UTC](https://discourse.julialang.org/t/multivariate-empirical-characteristic-function/63311/1 "2021-06-21T16:21:11Z")

</div>

Hi,

I am a Pythonista, yet totally new to Julia though.

Could someone, please, demonstrate an example on how to code an empirical characteristic function (ideally multivariate) in Julia-way?

That is, let’s say, we’ve got a matrix `X` of observations (`m` rows by `n` columns, where `m` is number of observations, `n` is dimension). So that, one could do smth like this:

```julia
ecf = estimate_ecf(X)
println(ecf(t))

```

P.S. I assume, that cf() from Distributions.jl isn’t much suitable for this

---

<div class="post-metadata">

**Author:** ![nateybear](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nateybear/32/20645_2.png) [@nateybear](https://discourse.julialang.org/u/nateybear)\
**Post date:** [June 21, 2021, 7:29pm UTC](https://discourse.julialang.org/t/multivariate-empirical-characteristic-function/63311/2 "2021-06-21T19:29:50Z")

</div>

Hello,

If I understand the formula for the empirical characteristic function correctly, then it should just be

```julia
using Statistics: mean
estimate_ecf(X) = t -> mean(exp.(im * t .* X); dims=1)
# example
X = randn(20, 2)
ecf = estimate_ecf(X)
println(ecf(t))
# 1×2 Array{Complex{Float64},2}:
# 1.0+0.0im 1.0+0.0im

```