Fitted theoretical distributions

For data values with histograms close to some known distribution, the user may choose to represent the data by fitting a theoretical distribution to the values. This will only work well if the histogram closely resembles a theoretical distribution.

Generic constructor

UncertainValue(empiricaldata::AbstractVector{T},
    d::Type{D}) where {D <: Distribution}

Type documentation

Examples

using Distributions, UncertainData

# Create a normal distribution
d = Uniform()

# Draw a 1000-point sample from the distribution.
some_sample = rand(d, 1000)

# Define an uncertain value by fitting a uniform distribution to the sample.
uv = UncertainValue(Uniform, some_sample)

using Distributions, UncertainData

# Create a normal distribution
d = Normal()

# Draw a 1000-point sample from the distribution.
some_sample = rand(d, 1000)

# Represent the uncertain value by a fitted normal distribution.
uv = UncertainValue(Normal, some_sample)

using Distributions, UncertainData

# Generate 1000 values from a gamma distribution with parameters α = 2.1,
# θ = 5.2.
some_sample = rand(Gamma(2.1, 5.2), 1000)

# Represent the uncertain value by a fitted gamma distribution.
uv = UncertainValue(Gamma, some_sample)

In these examples we're trying to fit the same distribution to our sample as the distribution from which we draw the sample. Thus, we will get good fits. In real applications, make sure to always visually investigate the histogram of your data!

Beware: fitting distributions may lead to nonsensical results!

In a less contrived example, we may try to fit a beta distribution to a sample generated from a gamma distribution.

using Distributions, UncertainData

# Generate 1000 values from a gamma distribution with parameters α = 2.1,
# θ = 5.2.
some_sample = rand(Gamma(2.1, 5.2), 1000)

# Represent the uncertain value by a fitted beta distribution.
uv = UncertainValue(Beta, some_sample)

This is obviously not a good idea. Always visualise your distribution before deciding on which distribution to fit! You won't get any error messages if you try to fit a distribution that does not match your data.

If the data do not follow an obvious theoretical distribution, it is better to use kernel density estimation to define the uncertain value.