Scale parameter in random.exponential()

[EngineerKhan]

Like Numpy's version, there should be a scale (β) provision in jax.random.exponential() as well.

[jakevdp]

We've opted not to have an extra parameter, because it's quite easy to scale the results yourself. For example, if you write this in numpy:

x = np.random.exponential(scale=10, size=(1000,))

the equivalent in JAX is this:

x = 10 * jax.random.exponential(key, shape=(1000,))

[EngineerKhan]

The exponential is defined as ​​​λ*e^-​​​λx. So just multiplying by ​​​λ won't do. I have confirmed it too:

Z = 10*random.exponential(key,(100,100))
print(X.mean(0).mean(0))

And it prints something in the range of 1.00 to 1.10 no matter what do I set the value of λ there.

[jakevdp]

That is the formula for the PDF of the exponential – for the sampled values it's a simple scaling:

from jax import random
key = random.PRNGKey(0)
x = 10.0 * random.exponential(key, shape=(100000,))
print(x.mean(), x.std())
# 10.040896 10.021657

[EngineerKhan]

Oh my bad. One question: Can you please explain that why does it show a whole matrix whenever I call the x.mean() there (no matter which distribution):

X = 10.0*random.exponential(key,(100,100))
print("The matrix's mean is: ",Z.mean)

[jakevdp]

You are writing Z.mean instead of Z.mean(); the former displays information about the mean method, which often includes the full representation of the array or matrix:

>>> x = jnp.arange(4)                                                                                                                          
>>> x.mean                                                                                                                                     
<bound method mean of DeviceArray([0, 1, 2, 3], dtype=int32)>

The latter will compute the mean:

>>> x.mean()                                                                                                                                   
DeviceArray(1.5, dtype=float32)