The Nakagami distribution [38] is defined by

where is a shape parameter, and controls the spread of the distribution. The distribution has a mean value defined by

and a mean square value defined by

resulting in a variance

The cumulative distribution function can be defined by the expression

Making the substitution of variable, , we obtain the expression

From [97, 3.381 (1)] we obtain

the incomplete gamma function. Numerical solutions for this expression can be obtained using a series expression of or selected according to which will give the fastest convergence [98, chapter 6].

Dave.Laurenson@ed.ac.uk