The `fitur`

package includes several tools for visually inspecting how good of a fit a distribution is. To start, fictional empirical data is generated below. Typically this would come from a *real-world* dataset such as the time it takes to serve a customer at a bank, the length of stay in an emergency department, or customer arrivals to a queue.

```
set.seed(438)
<- rweibull(10000, shape = 5, scale = 1) x
```

Below is a histogram showing the shape of the distribution and the y-axis has been set to show the probability density.

```
<- data.frame(x)
dt <- 30
nbins <- ggplot(dt, aes(x)) +
g geom_histogram(aes(y = ..density..),
bins = nbins, fill = NA, color = "black") +
theme_bw() +
theme(panel.grid = element_blank())
g
```

Three distributions have been chosen below to test against the dataset. Using the `fit_univariate`

function, each of the distributions are fit to a *fitted* object. The first item in each of the *fits* is the probabilty density function. Each *fit* is overplotted onto the histogram to see which distribution fits best.

```
<- c('gamma', 'lnorm', 'weibull')
dists <- lapply(dists, fit_univariate, x = x) multipleFits
```

```
## $start.arg
## $start.arg$shape
## [1] 18.97398
##
## $start.arg$rate
## [1] 20.68217
##
##
## $fix.arg
## NULL
##
## $start.arg
## $start.arg$meanlog
## [1] -0.1162831
##
## $start.arg$sdlog
## [1] 0.2560369
##
##
## $fix.arg
## NULL
##
## $start.arg
## $start.arg$shape
## [1] 4.686591
##
## $start.arg$scale
## [1] 1.005784
##
##
## $fix.arg
## NULL
```

```
plot_density(x, multipleFits, 30) + theme_bw() +
theme(panel.grid = element_blank())
```

The next plot used is the quantile-quantile plot. The `plot_qq`

function takes a numeric vector *x* of the empirical data and sorts them. A range of probabilities are computed and then used to compute comparable quantiles using the `q`

distribution function from the *fitted* objects. A good fit would closely align with the abline y = 0 + 1*x. Note: the q-q plot tends to be more sensitive around the “tails” of the distributions.

```
plot_qq(x, multipleFits) +
theme_bw() +
theme(panel.grid = element_blank())
```

The Percentile-Percentile plot rescales the input data to the interval (0, 1] and then calculates the theoretical percentiles to compare. The `plot_pp`

function takes the same inputs as the Q-Q Plot but it performs on rescaling of x and then computes the percentiles using the `p`

distribution of the *fitted* object. A good fit matches the abline y = 0 + 1*x. Note: The P-P plot tends to be more sensitive in the middle of the distribution.

```
plot_pp(x, multipleFits) +
theme_bw() +
theme(panel.grid = element_blank())
```