MA206 – Probability & Statistics
Empirical Distribution Function (EDF)
What is an Empirical Distribution Function?
Definition 1
:
Let
x
1
,
x
2
,...,
x
n
be a random sample.
The
empirical distribution function
)
(
x
F
n
(called EDF for short) is a function of
x
which equals the fraction of
X
i
s that are less than or
equal to
x
for each
x
,
∞
≤
≤
∞

x
.
Informally, an Empirical Distribution Function (EDF) is a function representing
accumulating frequency of actual sample data.
The EDF will allow us to make inferences about
some aspect of the larger population.
In other words, we can use the EDF to make good guesses
about the population characteristics.
A Small Example
Let’s look at a simple example to see how the EDF is created and what it looks like.
In
this example, we are interested in the number of occupants in vehicles along the Eisenhower
Expressway in Chicago.
We are able to take the following small sample:
}
6
,
2
,
1
,
4
,
2
{
=
S
.
First,
let’s put the 5 observations into increasing order.
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 Spring '10
 N/A
 edf, empirical distribution function

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