UncertainValue(d::Distributions.Distribution)

Construct an uncertain value from an instance of a distribution. If a specific uncertain value type has not been implemented, the number of parameters is determined from the distribution and an instance of one of the following types is returned:

• UncertainScalarTheoreticalOneParameter
• UncertainScalarTheoreticalTwoParameter
• UncertainScalarTheoreticalThreeParameter

Examples

UncertainValue(Normal(0, 1))
UncertainValue(Gamma(4, 5.1))
UncertainValue(Binomial, 8, 0.2)

UncertainValue(distribution::Type{D}, a::T1, b::T2;
    kwargs...) where {T1<:Number, T2 <: Number, D<:Distribution}

Constructor for two-parameter distributions

UncertainValues are currently implemented for the following two-parameter distributions: Uniform, Normal, Binomial, Beta, BetaPrime, Gamma, and Frechet.

Arguments

• a, b: Generic parameters whose meaning varies depending on what distribution is provided. See the list below.
• distribution: A valid univariate distribution from Distributions.jl.

Precisely what a and b are depends on which distribution is provided.

• UncertainValue(Normal, μ, σ) returns an UncertainScalarNormallyDistributed instance.
• UncertainValue(Uniform, lower, upper) returns an UncertainScalarUniformlyDistributed instance.
• UncertainValue(Beta, α, β) returns an UncertainScalarBetaDistributed instance.
• UncertainValue(BetaPrime, α, β) returns an UncertainScalarBetaPrimeDistributed instance.
• UncertainValue(Gamma, α, θ) returns an UncertainScalarGammaDistributed instance.
• UncertainValue(Frechet, α, θ) returns an UncertainScalarFrechetDistributed instance.
• UncertainValue(Binomial, n, p) returns an UncertainScalarBinomialDistributed instance.

Keyword arguments

• nσ: If distribution <: Distributions.Normal, then how many standard deviations away from μ does lower and upper (i.e. both, because they are the same distance away from μ) represent?
• tolerance: A threshold determining how symmetric the uncertainties must be in order to allow the construction of Normal distribution (upper - lower > threshold is required).
• trunc_lower: Lower truncation bound for distributions with infinite support. Defaults to -Inf.
• trunc_upper: Upper truncation bound for distributions with infinite support. Defaults to Inf.

Examples

Normal distribution

Normal distributions are formed by using the constructor UncertainValue(μ, σ, Normal; kwargs...). This gives a normal distribution with mean μ and standard deviation σ/nσ (nσ must be given as a keyword argument).

# A normal distribution with mean = 2.3 and standard deviation 0.3.
UncertainValue(2.3, 0.3, Normal)

# A normal distribution with mean 2.3 and standard deviation 0.3/2.
UncertainValue(2.3, 0.3, Normal, nσ = 2)

# A normal distribution with mean 2.3 and standard deviation = 0.3,
truncated to the interval `[1, 3]`.
UncertainValue(2.3, 0.3, Normal, trunc_lower = 1.0, trunc_upper = 3.0)

Uniform distribution

Uniform distributions are formed using the UncertainValue(lower, upper, Uniform) constructor.

#  A uniform distribution on `[2, 3]`
UncertainValue(-2, 3, Uniform)

UncertainValue(distribution::Type{D}, a::T1, b::T2, c::T3;
    kwargs...) where {T1<:Number, T2<:Number, T3<:Number, D<:Distribution}

Constructor for three-parameter distributions

Currently implemented distributions are BetaBinomial.

Arguments

• a, b, c: Generic parameters whose meaning varies depending on what distribution is provided. See the list below.
• distribution: A valid univariate distribution from Distributions.jl.

Precisely what a, b and c are depends on which distribution is provided.

• UncertainValue(BetaBinomial, n, α, β) returns an UncertainScalarBetaBinomialDistributed instance.

Keyword arguments

• nσ: If distribution <: Distributions.Normal, then how many standard deviations away from μ does lower and upper (i.e. both, because they are the same distance away from μ) represent?
• tolerance: A threshold determining how symmetric the uncertainties must be in order to allow the construction of Normal distribution (upper - lower > threshold is required).
• trunc_lower: Lower truncation bound for distributions with infinite support. Defaults to -Inf.
• trunc_upper: Upper truncation bound for distributions with infinite support. Defaults to Inf.

Examples

BetaBinomial distribution

Normal distributions are formed by using the constructor UncertainValue(μ, σ, Normal; kwargs...). This gives a normal distribution with mean μ and standard deviation σ/nσ (nσ must be given as a keyword argument).

# A beta binomial distribution with n = 100 trials and parameters α = 2.3 and
# β = 5
UncertainValue(100, 2.3, 5, BetaBinomial)

Uncertain value represented by a beta binomial distribution.

Uncertain value represented by a beta distribution.

Uncertain value represented by a beta prime distribution.

Uncertain value represented by a binomial distribution.

Uncertain value represented by a Fréchet distribution.

Uncertain value represented by a gamma distribution.

Uncertain value represented by a normal distribution.

Uncertain value represented by a uniform distribution.