20-Gamma and Exponential distribution-31-Aug-2020Material I 31-Aug-2020 gamma and exponential distri

Gamma and Exponential
Distribution
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Exponential distribution is a special case of Gamma
distribution.
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Gamma and Exponentially distribution is a
distributions that arises naturally in processes for
which the waiting times between events are relevant.
It can be thought of as a waiting time between
Poisson distributed events.

Gamma and Exponential
Distribution
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To predict the wait time until future events.
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The exponential distribution predicts the wait time
until the *very first* event.
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The gamma distribution, on the other hand, predicts
the wait time until the *-th* event occurs.
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Gamma Distribution
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A continuous random variable X follows gamma
distribution with parameter and then its probability
density function is given by
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where
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Gamma Distribution
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gamma function. . .
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, .
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, for
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Note , n is integer.
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Exponential Distribution ~
Gamma(
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A continuous random variable X follows exponential
distribution with parameter then its probability
density function is given by
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where : (some book they use )
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Exponential Distribution
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To get some intuition for this interpretation of the
exponential distribution, suppose you are waiting for an
event to happen. For example, you are at a store and are
waiting for the next customer. In each millisecond, the
probability that a new customer enters the store is very