Explore the Beta Distribution Function with our free online calculator. Instantly compute Probability Density Function (PDF) and Cumulative Distribution Function (CDF) values for given alpha and beta parameters. Visualize the distribution shape and probabilities with an interactive chart, essential for statistical analysis, Bayesian inference, and project management applications.
Formula:
The Probability Density Function (PDF) of the Beta Distribution is:
f(x; α, β) = (xα-1 (1-x)β-1) / B(α, β)
Where:
xis the value (between 0 and 1)α(alpha) andβ(beta) are positive shape parametersB(α, β)is the Beta Function,B(α, β) = Γ(α)Γ(β) / Γ(α+β)Γis the Gamma Function
The Cumulative Distribution Function (CDF) is F(x; α, β), representing the integral of the PDF from 0 to x. Our calculator computes PDF, provides an approximation for CDF for a specific x, and generates a plot for both functions across the full range.