Distribution of a Gaussian distribution absolute value

[Sal]

absolute value of gaussian

Hi Community

How the absolute value of a gaussian distributed random variable is distributed?

Thanks in advance

Sal

 

[darock]

absolute gaussian distribution

absolute value of a Gaussian distribution is distributed the same way as the positive value of a Gaussian distribution.

Prob(Y<=y)= 2 Prob(X<=y) y>0
=0 y<0

This is only for zero mean Gaussian.

 

[Sal]

absolute value of gaussian distribution

Hi

Thanks for your reply, but your notation is difficult to understand. I guess you mean it is double the half gaussian distribution. What I want to know is the name of the new distribution (if there is any, haven't got one so far) expressed in therms of mean and variance of the original Gaussian distribution.

Thank you and sorry for my poor explanation in my first post.

Sal

 

[darock]

distribution of absolute value

Hey, I am sorry...I completely take back my answer.

Absolute value of a Gaussian leads to Rayleigh Distribution. The following link might be useful.

https://en.wikipedia.org/wiki/Rayleigh_distribution

 

[changfa]

gaussian absolute value

Hey, I am sorry...I completely take back my answer.

Absolute value of a Gaussian leads to Rayleigh Distribution. The following link might be useful.

h**p://en.wikipedia.org/wiki/Rayleigh_distribution

Sorry, this answer is misleading as well. The amplitude (absolute value) of "complex" Gaussian with independent real and imag component is Rayleigh. For uni-Gaussian, its absolute value follows another distribution with support [0,+inf) and the half Guassian shape. (Simple calculation from probability theory works.)