# Diagnostic Plots for Fitting Distributions" In fitur: Fit Univariate Distributions

```knitr::opts_chunk\$set(echo = TRUE, fig.height = 5, fig.width = 7)
library(fitur)
library(ggplot2)
```

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)
x <- rweibull(10000, shape = 5, scale = 1)
```

## Histogram

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

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

## Histogram vs Density Plot

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.

```dists <- c('gamma', 'lnorm', 'weibull')
multipleFits <- lapply(dists, fit_univariate, x = x)
plot_density(x, multipleFits, 30) + theme_bw() +
theme(panel.grid = element_blank())
```

## Q-Q Plot

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())
```

## P-P Plot

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())
```

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fitur documentation built on May 2, 2019, 6:37 a.m.