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{TidyDensity} is a comprehensive R package that makes working withrandom numbers and probability distributions easy, intuitive, and tidy.Whether you’re simulating data, exploring distributions, or performingstatistical analysis, TidyDensity provides a unified interface thatintegrates seamlessly with the tidyverse ecosystem.

• 35+ Probability Distributions: Generate random data from a widevariety of continuous and discrete distributions
• Tidy Output: All functions return tibbles with a consistent,predictable structure
• Rich Metadata: Each distribution includes density (d_),probability (p_), quantile (q_), and random generation (r_)components
• Beautiful Visualizations: Built-in plotting functions with supportfor multiple plot types
• Parameter Estimation: Estimate distribution parameters fromempirical data using MLE, MME, and MVUE methods
• Bootstrap Analysis: Perform bootstrap resampling with integratedplotting and analysis tools
• Mixture Models: Create and analyze mixture distributions
• Interactive Plots: Generate interactive visualizations with plotlyintegration

Install the released version fromCRAN:

install.packages("TidyDensity")

Or install the development version fromGitHub:

# install.packages("devtools")devtools::install_github("spsanderson/TidyDensity")

Generate random data from a normal distribution and visualize it:

library(TidyDensity)library(dplyr)library(ggplot2)# Generate data from normal distributiontn<- tidy_normal(.n=100,.mean=0,.sd=1,.num_sims=6)# View the tibble structuretn#> # A tibble: 600 × 7#>    sim_number     x       y    dx       dy      p       q#>    <fct>      <int>   <dbl> <dbl>    <dbl>  <dbl>   <dbl>#>  1 1              1 -0.626  -3.51 0.000235 0.266  -0.626#>  2 1              2  0.184  -3.37 0.000617 0.573   0.184#>  3 1              3 -0.836  -3.22 0.00147  0.202  -0.836#>  4 1              4  1.60   -3.07 0.00322  0.945   1.60#> # ... with 596 more rows

Alltidy_ distribution functions return a tibble with the followingcolumns:

• sim_number: Simulation identifier
• x: Index of generated point
• y: The randomly generated value
• dx: Density function x-values
• dy: Density function y-values (PDF)
• p: Cumulative probability (CDF)
• q: Quantile values

TidyDensity includestidy_autoplot() for quick, publication-readyvisualizations:

# Density plottidy_autoplot(tn,.plot_type="density")# Quantile plottidy_autoplot(tn,.plot_type="quantile")# Probability plottidy_autoplot(tn,.plot_type="probability")# QQ plottidy_autoplot(tn,.plot_type="qq")

When simulating many distributions, the legend is automatically hiddenfor clarity:

tn<- tidy_normal(.n=100,.num_sims=20)tidy_autoplot(tn,.plot_type="density")

TidyDensity supports 35+ probability distributions:

• Normal Family: Normal, Log-Normal, Inverse Normal
• Exponential Family: Exponential, Inverse Exponential
• Gamma Family: Gamma, Inverse Gamma
• Beta Family: Beta, Generalized Beta
• Pareto Family: Pareto, Inverse Pareto, Single Parameter Pareto,Generalized Pareto
• Weibull Family: Weibull, Inverse Weibull
• Burr Family: Burr, Inverse Burr
• Other: Cauchy, Chi-Square, F-Distribution, t-Distribution,Logistic, Paralogistic, Triangular, Uniform

• Bernoulli
• Binomial
• Zero-Truncated Binomial
• Geometric
• Zero-Truncated Geometric
• Hypergeometric
• Negative Binomial
• Poisson
• Zero-Truncated Poisson

Each distribution has a correspondingtidy_*() function, e.g.,tidy_beta(),tidy_gamma(),tidy_poisson().

Estimate distribution parameters from empirical data:

# Generate sample datax<-mtcars$mpg# Estimate normal distribution parametersest<- util_normal_param_estimate(x,.auto_gen_empirical=TRUE)# View parameter estimatesest$parameter_tbl#> # A tibble: 2 × 7#>   dist_type samp_size   min   max  mean method   shape_est#>   <chr>         <int> <dbl> <dbl> <dbl> <chr>        <dbl>#> 1 Gaussian         32  10.4  33.9  20.1 MLE/MME      6.03#> 2 Gaussian         32  10.4  33.9  20.1 MVUE         6.10# Compare empirical data with fitted distributionest$combined_data_tbl|>  tidy_combined_autoplot()

Perform bootstrap resampling for robust statistical inference:

# Bootstrap resamplingbs<- tidy_bootstrap(mtcars$mpg,.num_sims=2000)# Bootstrap statisticsbootstrap_stat<- tidy_bootstrap(mtcars$mpg)|>  bootstrap_unnest_tbl()|>  summarise(mean_est= mean(y),sd_est= sd(y),ci_lower= quantile(y,0.025),ci_upper= quantile(y,0.975)  )

Create mixture distributions by combining multiple distributions:

# Create a mixture of two normal distributionsmix<- tidy_mixture_density(.tbl_list=list(    tidy_normal(.n=100,.mean=-2,.sd=0.5),    tidy_normal(.n=100,.mean=2,.sd=0.5)  ),.mixture_type="add")tidy_autoplot(mix,.plot_type="density")

Work directly with your own data:

# Create empirical distribution from dataemp<- tidy_empirical(mtcars$mpg,.num_sims=5)# Plot empirical distributiontidy_autoplot(emp,.plot_type="density")

Compare multiple distributions with different parameters:

# Create multiple simulations with different parametersmulti<- tidy_multi_single_dist(.tidy_dist="tidy_normal",.param_list=list(list(.n=100,.mean=0,.sd=1),list(.n=100,.mean=0,.sd=2),list(.n=100,.mean=2,.sd=1)  ))tidy_autoplot(multi,.plot_type="density")

• Getting StartedVignette
• FunctionReference
• Package Website

Contributions are welcome! Here’s how you can help:

• 🐛 Report bugs or request features viaGitHubIssues
• 📝 Submit pull requests for bug fixes or new features
• 📖 Improve documentation or add examples
• ⭐ Star the repository to show your support

Please follow ourCode of Conduct whenparticipating in this project.

If you use TidyDensity in your research, please cite it:

citation("TidyDensity")

• 📖 Read thedocumentation
• 🐛 Report bugs atGitHubIssues
• 💬 Ask questions onGitHubDiscussions

Steven P. Sanderson II, MPH

• Email:spsanderson@gmail.com
• ORCID:0009-0006-7661-8247

MIT License - seeLICENSE.md for details