# Creates a delay distribution as the sum of two other delay distributions

Source:`R/dist.R`

`plus-.dist_spec.Rd`

This is done via convolution with `stats::convolve()`

. Nonparametric delays
that can be combined are processed together, and their cumulative
distribution function is truncated at a specified tolerance level, ensuring
numeric stability.

## Arguments

- e1
The first delay distribution (from a call to

`dist_spec()`

) to combine.- e2
The second delay distribution (from a call to

`dist_spec()`

) to combine.

## Value

A delay distribution representing the sum of the two delays
(with class `dist_spec()`

)

## Examples

```
# A fixed lognormal distribution with mean 5 and sd 1.
lognormal <- dist_spec(
mean = 1.6, sd = 1, max = 20, distribution = "lognormal"
)
lognormal + lognormal
#>
#> Fixed distribution with PMF [0.0036 0.017 0.036 0.052 0.063 0.068 0.07 0.068 0.065 0.062 0.057 0.053 0.048 0.044 0.04 0.037 0.033 0.03 0.027 0.025 0.022 0.018 0.014 0.011 0.0087 0.0068 0.0054 0.0042 0.0033 0.0026 0.002 0.0015 0.0012 0.00087 0.00063]
#>
# An uncertain gamma distribution with mean 3 and sd 2
gamma <- dist_spec(
mean = 3, sd = 2, mean_sd = 0.5, sd_sd = 0.5, max = 20,
distribution = "gamma"
)
lognormal + gamma
#>
#> Combination of delay distributions:
#> Fixed distribution with PMF [0.06 0.14 0.14 0.12 0.096 0.079 0.065 0.053 0.044 0.037 0.031 0.027 0.023 0.019 0.017 0.015 0.013 0.011 0.0099 0.0087]
#> Uncertain gamma distribution with (untruncated) mean 3 (SD 0.5) and SD 2 (SD 0.5)
#>
# Using tolerance parameter
EpiNow2:::dist_spec_plus(lognormal, lognormal, tolerance = 0.5)
#>
#> Fixed distribution with PMF [0.0071 0.033 0.071 0.1 0.12 0.14 0.14 0.14 0.13 0.12]
#>
```