Statistics for Process Control Engineers

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