Article
CDF (Cumulative Distribution Function)
by
Samir Amberkar
(published on 17-Jan-2019)
Definition
Say we have a measurable (real & random) variable. If distribution is all the values that this variable may take,
cumulative distribution would be all accumulative frequencies with which this variable take the said values
when sorted in ascending order.
More appropriate probability based definition of CDF may be found in [1] .
Example
Let us look at an example shown in picture below for more clarity; click to view in bigger size.
Plotting the data
Here Data is number of hits a certain college education page get during an academic year.
So "the variable" is number of hits.
There are 104 entries (hits registered by web server at 104 time points over an academic year).
Distribution curve show how the variable changed its value w.r.t. time points.
To get its cumulative distribution curve, values are sorted (column D) and
then cumulative frequencies (column E) are calculated against each value by simple formula of (number of times so far) divided by (total number of time points i.e. 104).
Check Entry#21 in the picture for clarity.
Plot of column D versus column E gives us cumulative distribution curve.
Fig "Distribution Example"
Interpreting the data with cumulative distribution
Red circled point correspond to (number of hits=5000, frequency=50%) and
blue circled point correspond to (number of hits=average=6449, frequency=60%).
This indicate that even though average is 6449, many of the hits (60%) are below average.
Also, half of the time, page received at least 5000 number of hits.
Based on further information/data, we may even deduct (more correctly rather than just based on average)
whether the page is popular in relation to other web pages !
