chapter  29
4 Pages

- Rayleigh Distribution

The Rayleigh distribution with the scale parameter b has the probability density function (pdf)

f(x|b) = x b2

exp

( −1 2

x2

b2

) , x > 0, b > 0.

The cumulative distribution function (cdf) is given by

F (x|b) = 1− exp ( −1 2

x2

b2

) , x > 0, b > 0. (29.1)

Letting F (x|b) = p, and solving (29.1) for x, we get the inverse distribution function as

F−1(p|b) = b √ −2 ln(1− p), 0 < p < 1, b > 0. (29.2)

We observe from the plots of pdfs in Figure 28.1 that the Rayleigh distribution is always right skewed.