# tomroh/fitur

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 --- title: "Diagnostic Plots for Fitting Distributions" author: "Thomas Roh" date: "December 17, 2017" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Diagnostic Plots for Fitting Distributions} %\VignetteEngine{knitr::rmarkdown} \usepackage[utf8]{inputenc} --- ```{r setup, include=FALSE} 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. ```{r stats} 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. ```{r histPlot} 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. ```{r densPlot} 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. ```{r qqplot} 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. ```{r ppplot} plot_pp(x, multipleFits) + theme_bw() + theme(panel.grid = element_blank()) ```