9.4.15 The exponential distribution
The probability density function for the exponential distribution: exponential exponentiald
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 command computes the exponential distribution.
exponentiald is a synonym for exponential.
-
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.
exponential(2.1,3.5)
Output:
The cumulative distribution function for the exponential distribution: exponential_cdf exponentiald_cdf
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.
The inverse distribution function for the exponential distribution: exponential_icdf exponentiald_icdf
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.
Input:
exponential_icdf(2.3,0.87)
Output: