Fits an integer adjusted distribution to a subsampled bootstrap of data and then integrates
the posterior samples into a single set of summary statistics. Can be used to generate a robust
reporting delay that accounts for the fact the underlying delay likely varies over time or that
the size of the available reporting delay sample may not be representative of the current case load.

```
bootstrapped_dist_fit(
values,
dist = "lognormal",
samples = 2000,
bootstraps = 10,
bootstrap_samples = 250,
max_value,
verbose = FALSE
)
```

## Arguments

- values
Integer vector of values.

- dist
Character string, which distribution to fit. Defaults to lognormal (`"lognormal"`

) but
gamma (`"gamma"`

) is also supported.

- samples
Numeric, number of samples to take overall from the bootstrapped posteriors.

- bootstraps
Numeric, defaults to 1. The number of bootstrap samples (with replacement)
of the delay distribution to take.

- bootstrap_samples
Numeric, defaults to 100. The number of samples to take in each bootstrap.
When the sample size of the supplied delay distribution is less than 100 this is used instead.

- max_value
Numeric, defaults to the maximum value in the observed data. Maximum delay to
allow (added to output but does impact fitting).

- verbose
Logical, defaults to `FALSE`

. Should progress messages be printed

## Value

A list summarising the bootstrapped distribution

## Examples

```
# \donttest{
# lognormal
delays <- rlnorm(500, log(5), 1)
out <- bootstrapped_dist_fit(delays,
samples = 1000, bootstraps = 10,
dist = "lognormal"
)
out
#> $mean
#> [1] 1.473848
#>
#> $mean_sd
#> [1] 0.09470087
#>
#> $sd
#> [1] 1.143309
#>
#> $sd_sd
#> [1] 0.070004
#>
#> $max
#> [1] 98
#>
# }
```