discrete_pmf: Discretised probability mass function

In epiforecasts/EpiNow2: Estimate Real-Time Case Counts and Time-Varying Epidemiological Parameters

Discretised probability mass function

Description

This function returns the probability mass function of a discretised and truncated distribution defined by distribution type, maximum value and model parameters.

Usage

discrete_pmf(
  distribution = c("exp", "gamma", "lognormal", "normal", "fixed"),
  params,
  max_value,
  tolerance,
  width
)

Arguments

distribution	A character string representing the distribution to be used (one of "exp", "gamma", "lognormal", "normal" or "fixed")
params	A list of parameters values (by name) required for each model. For the exponential model this is a rate parameter and for the gamma model this is alpha and beta.
max_value	Numeric, the maximum value to allow. Samples outside of this range are resampled.
tolerance	Numeric; the desired tolerance level. Any part of the cumulative distribution function beyond 1 minus this tolerance level is removed. Default: 0, i.e. use the full distribution.
width	Numeric, the width of each discrete bin.

Value

A vector representing a probability distribution.

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. https://doi.org/10.48550/arXiv.2405.08841 Park, S. W., et al., "Estimating epidemiological delay distributions for infectious diseases", medRxiv, 2024. https://doi.org/10.1101/2024.01.12.24301247

epiforecasts/EpiNow2 documentation built on Aug. 15, 2024, 8:12 a.m.