ABSTRACT
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.
