Mental Disorders vs Actual Distributions

630 Table of Common Distributions Geometric (p) min Xᵢ ΣX n = 1 Negative binomial (n, p) λ = n(1−p) n → ∞ Discrete uniform α = β = 1 Beta-binomial (n, α, β) p = α/(α + β) α + β → ∞ Hypergeometric (M, N, K) n = M/N, n = K ΣX Poisson (λ) λ = np n → ∞ Binomial (n, p) α = β = ∞ Bernoulli (p) Lognormal ΠXᵢ Normal (μ, σ²) eˣ log X X − μ/σ ΣXᵢ Normal (0, 1) μ + σX Beta (α, β) α = β = 1 Gamma (r, λ) X₁/(X₁ + X₂) α = β = ∞ Uniform e⁻ˣ −λ log X Chi-squared (ν) λ = r/ν = 1/2 λ = 2 λ = 2 ν = 2 Exponential (λ) min Xᵢ Xᵢ/(X₁ + X₂) Weibull (γ, λ) Double exponential Cauchy 1/X̄ ν → ∞ F (ν₁, ν₂) ν₁, ν₂ Xᵢ/νᵢ t (ν) ν = 1 Actual Distributions Mental Disorders Relationships among common distributions. Solid lines represent transformations and special cases, dashed lines represent limits. Adapted from Leemis (1986).

A diagram of common probability distributions is covered with red and green hand-drawn outlines. The red outline labels the entire chaotic chart “Mental Disorders,” while the green outline highlights a smaller central area as “Actual Distributions.” The joke compares the intimidating complexity of probability theory to mental disorders, making it useful as a reaction to confusing statistics, mathematics, or an overwhelming system.

• @profunctor_io / 9655 2024-01-03