ABSTRACT
In Chapter 2, the gamma distribution and its basic properties were introduced. A random variable X is said to have a (two parameter) gamma distribution with scale parameter β and shape parameter α provided the pdf of X is given as
f(x ∣∣α, β) = 1
βαΓ(α) xα−1e−x/β , 0 < x <∞, α > 0, β > 0 (7.1.1)
The above pdf includes the following special cases:
(i) If α = k/2, for any integer k, and β = 2, then we get the χ2k (Chi-square with k degrees of freedom ) pdf as
f(x ∣∣ k) = 1
2k/2Γ(k/2) xk/2−1e−x/2, 0 < x <∞, k > 0 (7.1.2)
(ii) If α = 1, then we obtain the exponential distribution with scale parameter β as discussed in Chapter 6.
