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Statistics for Process Control Engineers by Myke King

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Appendix 2Summary of Distributions

Included here are two tables, Table A2.1 for continuous distributions and Table A2.2 for discrete distributions. They list, in alphabetical order, all the distributions described in this book. Their purpose is to assist the reader in shortlisting the distributions that might be considered for a given dataset.

Table A2.1 Summary of continuous distributions

distribution lower bound upper bound PDF CDF QF shape parameters μ σ γ κ alternative names Excel function
Amoroso α α, β, δ1, δ2
anglit μ − πβ/4 μ + πβ/4 μ, β μ 0
arcsine (first kind) 0 1 0.5 0.125 0 −1.5
arcsine (second kind) −1 1 0
arctangent α α, β, δ 0
asymmetric Laplace −∞ α, β, δ
Balding–Nichols 0 1 μ, p μ
Bates 0 1 n 0
Benini xmin xmin, α, β
Benktander‐I 0 λ, δ
Benktander‐II 0 λ, δ
beta rectangular −∞ δ1, δ2, δ3
beta‐I 0 1 δ1, δ2 Feller–Pareto BETA.DIST
beta‐II 0 β β, δ1, δ2, δ3 beta primeinverted beta
beta‐IV xmin xmax xmin, xmax, δ1, δ2 beta subjective PERT BETA.DIST
Birnbaum–Saunders α α, β, δ fatigue life
bounded Pareto‐I xmin xmax xmin, xmax, δ
Bradford xmin xmax xmin, xmax, λ
Burr‐I −∞ uniform
Burr‐II generalised logistic
Burr‐III α α, β, δ1, δ2
Burr‐IV α

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