MathIsimple
Distribution Calculator

Distribution Transformation Calculator

Transform between different probability distribution families and explore their mathematical relationships

Distribution Transformation
Select source and target distributions to explore possible transformations
Known Transformations
Gamma Γ(α,λ)Exponential E(λ)

Condition: α = 1

Example: Γ(1, 2) → E(2)

Gamma Γ(α,λ)Chi-square χ²(n)

Condition: α = n/2, λ = 1/2

Example: Γ(3, 0.5) → χ²(6)

Beta B(a,b)Fisher Z(a,b)

Condition: X = Y/(1-Y)

Example: Beta(2,3) → Z(2,3)

F-distribution F(m,n)Fisher Z(m/2,n/2)

Condition: X = (m/n)F

Example: F(4,6) → Z(2,3)

Usage Tips
Check parameter constraints for each distribution
Some transformations require specific parameter values
Not all distribution pairs can be transformed
Understand the mathematical relationship behind transformations

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