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86 HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 2.29 Probability density functions for the Exponential Distribution
(A=1)The integral of (2.47), N(X), the cumulative density function for the
Exponential Distribution is given as:N(X)= 1 −EXP(−A∗X) (2.48)where: A=The single parametric input, equal to 1/L in the Poisson
Distribution. A must be greater than 0.
EXP( )=The exponential function.Figures 2.29 and 2.30 show the functions of the Exponential Distribu-
tion. Note that once you know A, the distribution is completely determined.where: A=The single parametric input, equal to 1/L in the Poisson
Distribution. A must be greater than 0.
EXP( )=The exponential function.Figures 2.29 and 2.30 show the functions of the Exponential Distribu-
tion. Note that once you know A, the distribution is completely determined.
The mean and variance of the Exponential Distribution are:Mean= 1 /A (2.49)
Variance= 1 /A^2 (2.50)