Computation of Gamma probabilities can be significantly simplified by thinking of a Gamma variable as the time between some rare events (i.e. Poisson Distribution)

Formula

for:

• 𝐺𝑎𝑚𝑚𝑎(𝛼,𝜆) variable 𝐓
• 𝑃𝑜𝑖𝑠𝑠𝑜𝑛(λt) variable 𝐗

then:

• 𝑃 {𝐓 > t} = 𝑃 {𝐗 < 𝛼}
• 𝑃 {𝐓 ≤ t} = 𝑃 {𝐗 ≥ 𝛼}