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5.3 Exponential Distribution
Shape: The exponential distribution is a 2-parameter distribution and covers any specified
average and standard deviation. It is represented by a single point with a skewness of 2 and
kurtosis of 9 (excess kurtosis of 6) on a skewness-kurtosis plot as shown below. It is at the
intersection of the gamma and Weibull distributions.
10
Kurtosis
Negative
Exponential
Exponential
Gamma
7
Negative
Gamma
Weibull
Negative
Weibull
4
1
-3
-2
-1
0
1
2
3
Skewness
Density Function: The density function of the exponential distribution is shown below:
f
1
ε=0
0.8
λ=1
0.6
λ=2
0.4
λ=3
λ=4
0.2
x
2
66
4
6
Chapter 5
8
10