ABSTRACT
The Rayleigh distribution is a positively skewed distribution, originally derived by Lord J. W. S. Rayleigh (1919) in connection with a study of acoustical problems. In its most general form, this distribution may be considered as the distribution of the distance X from the origin to a point (Y1 , Y2 , ••• , Y") in a p-dimensional Euclidean space, where the components Y; are independent random variables, each of which is normally distributed (0, u 2). The random variable X thus is
(9.1.1)
The cdf is F[p/2, x 2!2a2] where
The kth moment about the origin is
(9.1.4)
The expected value, variance, and mode are
Estimation in this chapter will be limited to truncated and censored samples. The calculation of estimates from complete samples has been adequately covered elsewhere. First, however, we examine special cases of interest to engineers, physicists, and other scientists as models for the analysis of data resulting from studies of wave propagation, radiation, target errors, velocities of gas particles, and related fields of inquiry.
