Describe and understand the world through data.

Data collection and data comparison are the foundations of scientific research. *Mathematics* provides the abstract framework to describe patterns we observe in nature and *Statistics* provides the framework to quantify the uncertainty of these patterns. In statistics, natural patterns are described in form of probability distributions which either follow a fixed pattern (parametric distributions) or more dynamic patterns (non-parametric distributions).

The `philentropy`

package implements fundamental distance and similarity measures to quantify distances between probability density functions as well as traditional information theory measures. In this regard, it aims to provide a framework for comparing natural patterns in a statistical notation.

This project is born out of my passion for statistics and I hope that it will be useful to the people who share it with me.

HG Drost, (2018).

Philentropy: Information Theory and Distance Quantification with R.Journal of Open Source Software, 3(26), 765. https://doi.org/10.21105/joss.00765

- Introduction to the philentropy package
- Distance and Similarity Measures implemented in philentropy
- Information Theory Metrics implemented in philentropy

```
[1] "euclidean" "manhattan" "minkowski"
[4] "chebyshev" "sorensen" "gower"
[7] "soergel" "kulczynski_d" "canberra"
[10] "lorentzian" "intersection" "non-intersection"
[13] "wavehedges" "czekanowski" "motyka"
[16] "kulczynski_s" "tanimoto" "ruzicka"
[19] "inner_product" "harmonic_mean" "cosine"
[22] "hassebrook" "jaccard" "dice"
[25] "fidelity" "bhattacharyya" "hellinger"
[28] "matusita" "squared_chord" "squared_euclidean"
[31] "pearson" "neyman" "squared_chi"
[34] "prob_symm" "divergence" "clark"
[37] "additive_symm" "kullback-leibler" "jeffreys"
[40] "k_divergence" "topsoe" "jensen-shannon"
[43] "jensen_difference" "taneja" "kumar-johnson"
[46] "avg"
```

```
# define a probability density function P
P <- 1:10/sum(1:10)
# define a probability density function Q
Q <- 20:29/sum(20:29)
# combine P and Q as matrix object
x <- rbind(P,Q)
# compute the jensen-shannon distance between
# probability density functions P and Q
distance(x, method = "jensen-shannon")
```

```
jensen-shannon using unit 'log'.
jensen-shannon
0.02628933
```

Alternatively, users can also retrieve values from all available distance/similarity metrics using `dist.diversity()`

:

```
euclidean manhattan
0.12807130 0.35250464
minkowski chebyshev
0.12807130 0.06345083
sorensen gower
0.17625232 0.03525046
soergel kulczynski_d
0.29968454 0.42792793
canberra lorentzian
2.09927095 0.49712136
intersection non-intersection
0.82374768 0.17625232
wavehedges czekanowski
3.16657887 0.17625232
motyka kulczynski_s
0.58812616 2.33684211
tanimoto ruzicka
0.29968454 0.70031546
inner_product harmonic_mean
0.10612245 0.94948528
cosine hassebrook
0.93427641 0.86613103
jaccard dice
0.13386897 0.07173611
fidelity bhattacharyya
0.97312397 0.03930448
hellinger matusita
0.32787819 0.23184489
squared_chord squared_euclidean
0.05375205 0.01640226
pearson neyman
0.16814418 0.36742465
squared_chi prob_symm
0.10102943 0.20205886
divergence clark
1.49843905 0.86557468
additive_symm kullback-leibler
0.53556883 0.13926288
jeffreys k_divergence
0.31761069 0.04216273
topsoe jensen-shannon
0.07585498 0.03792749
jensen_difference taneja
0.03792749 0.04147518
kumar-johnson avg
0.62779644 0.20797774
```

```
# install.packages("devtools")
# install the current version of philentropy on your system
library(devtools)
install_github("HajkD/philentropy", build_vignettes = TRUE, dependencies = TRUE)
```

The current status of the package as well as a detailed history of the functionality of each version of `philentropy`

can be found in the NEWS section.

`distance()`

: Implements 46 fundamental probability distance (or similarity) measures`getDistMethods()`

: Get available method names for ‘distance’`dist.diversity()`

: Distance Diversity between Probability Density Functions`estimate.probability()`

: Estimate Probability Vectors From Count Vectors

`H()`

: Shannon’s Entropy H(X)`JE()`

: Joint-Entropy H(X,Y)`CE()`

: Conditional-Entropy H(X | Y)`MI()`

: Shannon’s Mutual Information I(X,Y)`KL()`

: Kullback–Leibler Divergence`JSD()`

: Jensen-Shannon Divergence`gJSD()`

: Generalized Jensen-Shannon Divergence

I would be very happy to learn more about potential improvements of the concepts and functions provided in this package.

Furthermore, in case you find some bugs or need additional (more flexible) functionality of parts of this package, please let me know:

https://github.com/HajkD/philentropy/issues

or find me on twitter: HajkDrost