knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width = 7, fig.height = 5, fig.align = "center" ) # Putting this here too so that we don't have pkg startup messages. library(dplyr)

One statistic that cyclists might be interested to track is their Eddington
number. The Eddington number for cycling, *E*, is the maximum number where a
cyclist has ridden *E* miles in *E* days. So to get a number of 30, you need to
have ridden 30 miles or more on 30 separate days.

This package allows the user to compute Eddington numbers and more. For example,
users can determine if a specific Eddington number is satisfied or how many
rides of the appropriate distance are needed to increment their Eddington
number. It also contains **simulated** data to demonstrate the package use.

Loading the simulated data is simple. Let's take a quick look at the first few lines.

library(eddington) head(rides)

First, we need to establish the granularity of the data. As you can see above, there are at least two entries for 2009-01-18. Since this data simulates a rider who tracked each individual ride, there could be more than one ride per day in this dataset. Therefore, we need to transform the data to aggregate on day.

library(dplyr) days <- rides %>% group_by(ride_date) %>% summarize(n = n(), total = sum(ride_length)) head(days)

Let's just take a quick peek at the summary stats:

```
summary(days)
```

This plot provides a histogram of daily mileages. Note the summary Eddington number is in dark red---we'll see how that's calculated in the next section.

hist( as.integer(days$total), breaks = 30, main = "Histogram of Daily Mileages", xlab = "Miles" ) abline(v = E_num(days$total), col = "darkred") legend( "topright", legend = "Eddington Number", col = "darkred", bty = "n", lty = 1L )

To compute the Eddington number, we use the `E_num()`

function like so:

E_num(days$total)

To see how the Eddington number progressed over the year, use `E_cum()`

. It can
be useful to add the vector as a new column onto the existing dataset:

days$E <- E_cum(days$total) head(days)

It might be more interesting to see that graphically:

E <- E_num(days$total) E_contribs <- days[days$total >= E,] plot( y = days$total, x = days$ride_date, type = "h", main = "Ride Mileages in 2009", xlab = "Ride Day", ylab = "Total Miles", bty = "n", ylim = c(0, 90) ) lines( y = c(0, days$E), x = c(as.Date("2009-01-01"), days$ride_date), type = "s", col = "darkred" ) abline(h = E, lty = 2L, col = "darkred") text( E_contribs[,c("ride_date","total")], labels = as.integer(E_contribs[["total"]]), pos = 3, cex = 0.7 ) legend( "topleft", title = "Eddington Number", legend = c("Cumulative", "Summary"), col = "darkred", bty = "n", lty = c(1L, 2L) )

So now that we know that the summary Eddington number was 29 for the year, let's
see how many more rides of length 30 or greater that we would have needed to
increment the *E* to 30.

E_next(days$total)

An ambitious rider might be interested to see the number of rides required to
reach a stretch goal. Say, how many more rides would have been needed to reach
an *E* of 50? For that, we use `E_req()`

, which stands for "required."

E_req(days$total, 50)

We could also check to see if we've gotten to 30 by using `E_sat()`

, which
stands for "satisfies."

E_sat(days$total, 30)

The text above should give you a good start in using the `eddington`

package.
Although this package was developed with bicycling in mind, it has applications
for other users as well. The Eddington number is a specific application of
computing the side length of a Durfee square. Another application is the Hirsch
index, or *h*-index, which a popular number in bibliometrics.

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