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1
Beyond the Normal Distribution
•
Normal Distribution --- N(
,
2
)
•
Continuous distribution, defined on entire real line (allows positive
density on negative numbers, even though it may be negligible)
•
Symmetric
•
What if we want to model a phenomena that has a skewed
distribution? [For example taking all values in (0,
)
•
Income
[Economics, Management]
•
Time until the next “hit” on a web page [Web Data Mining
•
Response time to a stimulus [Psychology]
•
Lifetime of a component of a device [reliability studies]
•
Inter-arrival times of events [Transportation, Reliability, Queuing]
•
A flexible “family” of distributions is used to model these phenomena
•
The family can represent a large variety of shapes
Section 4.4
Gamma, Exponential and
2
Distributions
Gamma Distribution
:
X
Gamma(
,
)
Flexible, two-parameter family of distributions.
Special Cases:
Exponential Distribution:
X
Exp(
)
Chi-Squared Distribution:
X
2

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Gamma Distribution

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