Question

Difference between rayleigh and gaussian distribution

Answer 1

Answer:

really and boosting distribution are the similar but their formulas are different

Answer 2

Step-by-step explanation:

Take a complex number z=u+iv and call its magnitude x.

Consider the real and imaginary parts to be Gaussian distributed:

fU(u)=12πσ2−−−−√exp(−u22σ2)

and similarily for v.

Then the magnitude of z is distributed as

f(x,σ)=12πσ2∫∞−∞du∫∞−∞dvexp(−u22σ2)exp(−v22σ2)δ(x−u2+v2−−−−−−√)

if we convert to polar co-ordinates then evaluate we have

f(x,σ)=xσ2exp(−x22σ2)

which is the Rayleigh distribution.

Can anyone explain where the second expression for f(x,σ) comes from? How is this the distribution of the length of z