# fit_disc_gamma: Fit discretised distributions using ML In epitrix: Small Helpers and Tricks for Epidemics Analysis

## Description

These functions performs maximum-likelihood (ML) fitting of a discretised distribution. This is typically useful for describing delays between epidemiological events, such as incubation period (infection to onset) or serial intervals (primary to secondary onsets). The function `optim` is used internally for fitting.

## Usage

 `1` ```fit_disc_gamma(x, mu_ini = 1, cv_ini = 1, interval = 1, w = 0, ...) ```

## Arguments

 `x` A vector of numeric data to fit; NAs will be removed with a warning. `mu_ini` The initial value for the mean 'mu', defaulting to 1. `cv_ini` The initial value for the coefficient of variation 'cv', defaulting to 1. `interval` The interval used for discretisation; see `distcrete`. `w` The centering of the interval used for discretisation; see `distcrete`. `...` Further arguments passed to `optim`.

## Value

The function returns a list with human-readable parametrisation of the discretised Gamma distibution (mean, sd, cv), convergence indicators, and the discretised Gamma distribution itself as a `distcrete` object (from the `distcrete` package).

## Author(s)

Thibaut Jombart [email protected]

The `distcrete` package for discretising distributions, and `optim` for details on available optimisation procedures.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## generate data mu <- 15.3 # days sigma <- 9.3 # days cv <- mu / sigma cv param <- gamma_mucv2shapescale(mu, cv) if (require(distcrete)) { w <- distcrete("gamma", interval = 1, shape = param\$shape, scale = param\$scale, w = 0) x <- w\$r(100) x fit_disc_gamma(x) } ```