18.4.15 Exponential distribution
The probability density function for the exponential distribution.
The exponential distribution depends on one parameters, λ>0;
the value of the density function at x ≥ 0 is
exponential(λ,x)=λ e−λ x.
The exponential
or exponentiald
command computes the exponential distribution.
-
exponential takes two arguments:
-
λ, a positive number (the parameter).
- x, a positive number.
- exponential(λ,x) returns the value of the
exponential density function with parameter λ at x; namely,
exponential(λ,x)=λ e−λ x.
Example
The cumulative distribution function for the exponential distribution.
The exponential_cdf
(or exponentiald_cdf)
command computes the cumulative distribution function for the exponential distribution.
-
exponential_cdf (or exponentiald_cdf)
takes two arguments:
-
λ, a positive number (the parameter).
- x, a positive number.
- exponential_cdf(λ,x) returns
Prob(X ≤ x) for the exponential distribution with
parameter λ.
- exponential_cdf(λ,x,y) returns
Prob(x ≤ X ≤ y).
Examples
exponential_cdf(2.3,0.9,3.2) |
The inverse distribution function for the exponential distribution.
The exponential_icdf
(or exponentiald_icdf)
command computes the inverse distribution for the exponential distribution.
-
exponential_icdf (or exponentiald_icdf) takes two
arguments:
-
λ, a positive number (the parameter).
- h, a positive real number.
- exponential_icdf(λ,h) returns the inverse
distribution for the exponential distribution with parameter
λ; namely, the value of x for which
Prob(X ≤ x)=h.
Example
exponential_icdf(2.3,0.87) |