A.1. Continuous Distributions

A.1.1. Normal

Mean = µ

Variance = σ²

Parameters:

µ: mean,

σ: standard deviation,

A.1.2. Student’s t

Mean = 0

Variance = n/(n-2), n > 2

where X has a standard normal distribution. Mean and standard deviation parameters are needed if X has a non-standard normal distribution.

Parameters:

µ: mean,

σ: standard deviation,

n: degrees of freedom,

A.1.3. Chi-Square

Mean = n

Variance = 2n

Parameter:

n: degrees of freedom,

A.1.4. F

Mean = q/(q-2), q > 2

Variance = 2q²(p+q-2)/p(q-2)²(q-4), q > 4

Parameters:

p: numerator degrees of freedom,

q: denominator degrees of freedom,

A.1.5. Beta

Mean = α/(α+β)

Variance = αβ/((α+β)²(α+β+1))

Parameters:

α: alpha,

β: beta,

A.1.6. Gamma

Mean = αβ

Variance = αβ²

Parameters:

α: alpha shape,

β: beta scale,

A.1.7. Uniform

Mean = (M+N)/2

Variance = (N-M)²/12

Parameters:

M: lower bound

N: upper bound,

A.1.8. Triangular

Mean = (M+O+N)/3

Variance = (M2+O2+N2-MO-MN-ON)/18

Parameters:

M: lower bound

O: centre

N: upper bound,

A.1.9. Lognormal

Mean = Exp(µ+σ 2/2)

Variance = Exp(2µ+σ 2)(Exp(σ 2)-1)

Parameters:

µ: mean,

σ: standard deviation,

A.1.10. Exponential

Mean = 1/β

Variance = 1/β2

Parameter:

β: 1/mean,

A.1.11. Erlang

Mean = 1/β

Variance = α/β2

Parameters:

α: alpha shape,

β: beta scale,

A.1.12. Weibull

Mean = (1/β)1/a G(1+1/α)

Variance = β–2/a [G(1+2/α)-G2(1+1/α)]

Parameters:

α: alpha shape,

β: beta,