# Fit an Integer Adjusted Exponential, Gamma or Lognormal distributions

Source:`R/estimate_delay.R`

`dist_fit.Rd`

## Usage

```
dist_fit(
values = NULL,
samples = 1000,
cores = 1,
chains = 2,
dist = "exp",
verbose = FALSE,
backend = "rstan"
)
```

## Arguments

- values
Numeric vector of values

- samples
Numeric, number of samples to take. Must be >= 1000. Defaults to 1000.

- cores
Numeric, defaults to 1. Number of CPU cores to use (no effect if greater than the number of chains).

- chains
Numeric, defaults to 2. Number of MCMC chains to use. More is better with the minimum being two.

- dist
Character string, which distribution to fit. Defaults to exponential (

`"exp"`

) but gamma (`"gamma"`

) and lognormal (`"lognormal"`

) are also supported.- verbose
Logical, defaults to FALSE. Should verbose progress messages be printed.

- backend
Character string indicating the backend to use for fitting stan models. Supported arguments are "rstan" (default) or "cmdstanr".

## Examples

```
# \donttest{
# integer adjusted exponential model
dist_fit(rexp(1:100, 2),
samples = 1000, dist = "exp",
cores = ifelse(interactive(), 4, 1), verbose = TRUE
)
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 1).
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1:
#> Chain 1: Gradient evaluation took 4.8e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.48 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
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#> Chain 1: 0.26 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 2).
#> Chain 2: Rejecting initial value:
#> Chain 2: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 2: Stan can't start sampling from this initial value.
#> Chain 2:
#> Chain 2: Gradient evaluation took 4.6e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.46 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
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#> Chain 2:
#> Chain 2: Elapsed Time: 0.178 seconds (Warm-up)
#> Chain 2: 0.089 seconds (Sampling)
#> Chain 2: 0.267 seconds (Total)
#> Chain 2:
#> Inference for Stan model: dist_fit.
#> 2 chains, each with iter=1500; warmup=1000; thin=1;
#> post-warmup draws per chain=500, total post-warmup draws=1000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> lambda[1] 2.81 0.02 0.49 1.96 2.50 2.76 3.10 3.96 432 1.00
#> lp__ -13.12 0.04 0.75 -15.18 -13.32 -12.80 -12.64 -12.60 371 1.02
#>
#> Samples were drawn using NUTS(diag_e) at Fri Jun 7 12:55:24 2024.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
# integer adjusted gamma model
dist_fit(rgamma(1:100, 5, 5),
samples = 1000, dist = "gamma",
cores = ifelse(interactive(), 4, 1), verbose = TRUE
)
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000304 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 3.04 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000303 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 3.03 seconds.
#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2:
#> Chain 2: Elapsed Time: 2.845 seconds (Warm-up)
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#> Chain 2: 3.921 seconds (Total)
#> Chain 2:
#> WARN [2024-06-07 12:55:32] dist_fit (chain: 1): Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess -
#> WARN [2024-06-07 12:55:32] dist_fit (chain: 1): Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess -
#> Inference for Stan model: dist_fit.
#> 2 chains, each with iter=1500; warmup=1000; thin=1;
#> post-warmup draws per chain=500, total post-warmup draws=1000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> alpha_raw[1] 0.79 0.04 0.51 0.06 0.41 0.74 1.11 1.90 181 1.00
#> beta_raw[1] 0.96 0.04 0.53 0.13 0.56 0.87 1.27 2.13 203 1.00
#> alpha[1] 6.42 0.04 0.51 5.69 6.03 6.36 6.74 7.53 181 1.00
#> beta[1] 6.78 0.04 0.53 5.96 6.39 6.69 7.09 7.95 203 1.00
#> lp__ -11.38 0.10 1.12 -14.20 -11.91 -11.06 -10.58 -10.15 132 1.01
#>
#> Samples were drawn using NUTS(diag_e) at Fri Jun 7 12:55:32 2024.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
# integer adjusted lognormal model
dist_fit(rlnorm(1:100, log(5), 0.2),
samples = 1000, dist = "lognormal",
cores = ifelse(interactive(), 4, 1), verbose = TRUE
)
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 1).
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1:
#> Chain 1: Gradient evaluation took 7.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.73 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
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#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 6.6e-05 seconds
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#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2: 0.565 seconds (Total)
#> Chain 2:
#> Inference for Stan model: dist_fit.
#> 2 chains, each with iter=1500; warmup=1000; thin=1;
#> post-warmup draws per chain=500, total post-warmup draws=1000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> mu[1] 1.60 0.00 0.02 1.55 1.59 1.60 1.62 1.65 636 1.00
#> sigma[1] 0.19 0.00 0.02 0.15 0.17 0.19 0.20 0.22 612 1.01
#> lp__ -82.06 0.05 1.05 -84.86 -82.49 -81.69 -81.32 -81.08 457 1.00
#>
#> Samples were drawn using NUTS(diag_e) at Fri Jun 7 12:55:34 2024.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
# }
```