PERT Distribution

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

where B is the Beta function.

• Range 𝑙𝑏 ≤ 𝑥 ≤ 𝑢𝑏
• Parameter 𝑙𝑏: 𝑙𝑏 < 𝑧_min, the lower bound of 𝑧
• Parameter 𝑢𝑏: 𝑧_max < 𝑢𝑏, the upper bound of 𝑧
• Parameter 𝜂: 𝑙𝑏 < 𝜂 < 𝑢𝑏, the mode of 𝑧

Notes: The PERT argument 𝑧 and the three parameters, 𝑙𝑏, 𝑢𝑏 and 𝜂 are transformed using the PERT transform; the resulting argument, 𝑥 is distributed Beta, with shape parameters 𝛼 and 𝛽.