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日期：2024-03-03 08:34

Exponential Distribution

February 24, 2021

• The Probability Density Function(PDF) of the exponential random variable t is given

by:

f(t) = λe−λt, t ≥ 0

• Mean= 1/λ

• The Cumulative Distribution Function(CDF) :

F(t) = f(T ≤ t) = 1 − e

−λt t ≥ 0

• Inverse transform sampling is a basic method for generating sample numbers at random

from any probability distribution given its cumulative distribution function. This means by

knowing the value of F(t) we can find the value of t as follows:

t = −

1

λ

ln(1 − F(t))

In Jave, the value of F(t) can be generated using nextDouble() function which returns the

next pseudorandom, uniformly distributed value between 0 and 1 from this random number

generator’s sequence.

• Example

Generate an arrival time from an exponential distribution of mean 3, if nextDouble()

returns 0.811. Sol. the arrival time value t can be found by substituting t=0.811 in the

above equation:

t = −

1

λ

ln(1 − F(t)) = −

1

3

ln(1 − 0.811) = 5

1