Discretise a <dist_spec>

Usage

# S3 method for class 'dist_spec'
discretise(x, strict = TRUE, ...)

discretize(x, ...)

Arguments

x

A <dist_spec>

strict

Logical; If TRUE (default) an error will be thrown if a distribution cannot be discretised (e.g., because no finite maximum has been specified or parameters are uncertain). If FALSE then any distribution that cannot be discretised will be returned as is.

...

ignored

Value

A <dist_spec> where all distributions with constant parameters are nonparametric.

Methodological details

The probability mass function of the discretised probability distribution is a vector where the first entry corresponds to the integral over the (0,1] interval of the corresponding continuous distribution (probability of integer 0), the second entry corresponds to the (0,2] interval (probability mass of integer 1), the third entry corresponds to the (1, 3] interval (probability mass of integer 2), etc. This approximates the true probability mass function of a double censored distribution which arises from the difference of two censored events.

References

Charniga, K., et al. “Best practices for estimating and reporting epidemiological delay distributions of infectious diseases using public health surveillance and healthcare data”, arXiv e-prints, 2024. doi:10.48550/arXiv.2405.08841 Park, S. W., et al., "Estimating epidemiological delay distributions for infectious diseases", medRxiv, 2024. doi:10.1101/2024.01.12.24301247

Examples

# A fixed gamma distribution with mean 5 and sd 1.
dist1 <- Gamma(mean = 5, sd = 1, max = 20)

# An uncertain lognormal distribution with mean 3 and sd 2
dist2 <- LogNormal(mean = Normal(3, 0.5), sd = Normal(2, 0.5), max = 20)
#> Warning: ! Uncertain lognormal distribution specified in terms of parameters that are
#>   not the "natural" parameters of the distribution meanlog and sdlog.
#> ℹ Converting using a crude and very approximate method that is likely to
#>   produce biased results.
#> ℹ If possible it is preferable to specify the distribution directly in terms of
#>   the natural parameters.

# The maxf the sum of two distributions
discretise(dist1 + dist2, strict = FALSE)
#> Composite distribution:
#> - nonparametric distribution
#>   PMF: [8e-11 2.3e-05 0.0056 0.078 0.26 0.34 0.22 0.076 0.016 0.0022 0.00022 1.7e-05 1.1e-06 5.5e-08 2.4e-09 9.2e-11 3.2e-12 9.7e-14 2.8e-15 0 0]
#> - lognormal distribution (max: 20):
#>   meanlog:
#>     - normal distribution:
#>       mean:
#>         0.91
#>       sd:
#>         0.31
#>   sdlog:
#>     - normal distribution:
#>       mean:
#>         0.61
#>       sd:
#>         0.25