Can you please explain me why we have two different PDFs for Rayleigh distribution as follows,
1) $(x/\sigma^2 ) \times e^{-x^2/2\sigma^2}$
and
2) $(2x/\sigma^2) \times e^{-x^2/\sigma^2}$
thank you for your help.
2026-03-25 17:45:19.1774460719
PDF of Rayleigh distribution
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They are equivalent to each other, but just different parametrizations. You try to substitute $\sigma^2$ by $s^2/2$ into the first parametrization, then you will get the second form.