exponential

exponential(lambda: number) 🡒 ranvar, pure function

Returns a probability distribution over $\mathbb{Z}$ obtained from the CDF of the exponential distribution with:

$$P_\lambda[X = n] = F(n; \lambda) - F(n - 1; \lambda) $$

with

$$F(x;\lambda) = 1-e^{-\lambda x} \text{ if } x \ge 0 \text{ else } 0$$

The argument lambda must be positive or the function fails.

Example:

table T = with
  [| as N |]
  [|  0.5 |]
  [|  1.5 |]
  [|  2.5 |]

show table "" a1b4 with
  T.N
  exponential(T.N)

See also