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Uncertain values may be constructed in three different ways, depending on what information you have available. You may represent an uncertain value by

Examples

If the data doesn't follow an obvious theoretical distribution, the recommended course of action is to represent the uncertain value with a kernel density estimate of the distribution.

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using Distributions, UncertainData, KernelDensity

# Generate some random data from a normal distribution, so that we get a
# histogram resembling a normal distribution.
some_sample = rand(Normal(), 1000)

# Uncertain value represented by a kernel density estimate (it is inferred
# that KDE is wanted when no distribution is provided to the constructor).
uv = UncertainValue(some_sample)

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using Distributions, UncertainData

# Generate some random data from a normal distribution, so that we get a
# histogram resembling a normal distribution.
some_sample = rand(Normal(), 1000)



# Specify that we want a kernel density estimate representation
uv = UncertainValue(UnivariateKDE, some_sample)

If your data has a histogram closely resembling some theoretical distribution, the uncertain value may be represented by fitting such a distribution to the data.

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using Distributions, UncertainData

# Generate some random data from a normal distribution, so that we get a
# histogram resembling a normal distribution.
some_sample = rand(Normal(), 1000)

# Uncertain value represented by a theoretical normal distribution with
# parameters fitted to the data.
uv = UncertainValue(Normal, some_sample)

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using Distributions, UncertainData

# Generate some random data from a gamma distribution, so that we get a
# histogram resembling a gamma distribution.
some_sample = rand(Gamma(), 1000)

# Uncertain value represented by a theoretical gamma distribution with
# parameters fitted to the data.
uv = UncertainValue(Gamma, some_sample)

It is common when working with uncertain data found in the scientific literature that data value are stated to follow a distribution with given parameters. For example, a data value may be given as normal distribution with a given mean μ = 2.2 and standard deviation σ = 0.3.

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# Uncertain value represented by a theoretical normal distribution with
# known parameters μ = 2.2 and σ = 0.3
uv = UncertainValue(Normal, 2.2, 0.3)

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# Uncertain value represented by a theoretical gamma distribution with
# known parameters α = 2.1 and θ = 3.1
uv = UncertainValue(Gamma, 2.1, 3.1)

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# Uncertain value represented by a theoretical binomial distribution with
# known parameters p = 32 and p = 0.13
uv = UncertainValue(Binomial, 32, 0.13)