EXPON.DIST Function (LibreOffice Calc)

• Computes the exponential distribution
• Supports PDF (probability density) and CDF (cumulative probability)
• Used in reliability engineering, queueing theory, and stochastic modeling
• Models time between independent events

EXPON.DIST(x; lambda; cumulative)

Arguments

• x:
  The value at which to evaluate the distribution (time ≥ 0).

• lambda:
  The rate parameter (events per unit time).
  Must be > 0.

• cumulative:

  • TRUE → return CDF
  • FALSE → return PDF

PDF (cumulative = FALSE)

[ f(x) = \lambda e^{-\lambda x} ]

CDF (cumulative = TRUE)

[ F(x) = 1 - e^{-\lambda x} ]

PDF example

=EXPON.DIST(2; 0.5; FALSE)
→ 0.18393972

CDF example

=EXPON.DIST(2; 0.5; TRUE)
→ 0.63212056

Probability that event occurs within 10 minutes

=EXPON.DIST(10; lambda; TRUE)

Probability density at x = 0

=EXPON.DIST(0; 0.2; FALSE)
→ 0.2

Reliability modeling (time to failure)

=1 - EXPON.DIST(t; lambda; TRUE)
→ survival probability

Mean time between failures (MTBF)

Given MTBF = 1/lambda:

=EXPON.DIST(t; 1/MTBF; TRUE)

Probability event occurs between a and b

=EXPON.DIST(b; λ; TRUE) - EXPON.DIST(a; λ; TRUE)

Generate exponential random variable

=-LN(1 - RAND()) / lambda

Queueing theory (M/M/1 arrival times)

=EXPON.DIST(t; arrival_rate; TRUE)

Hazard rate (constant for exponential)

=lambda

Convert rate to mean lifetime

=1 / lambda

EXPON.DIST returns a number

Behavior details

• x must be ≥ 0
• lambda must be > 0
• PDF always ≥ 0
• CDF ranges from 0 → 1
• Exponential distribution has memoryless property:
  [ P(X > s + t \mid X > s) = P(X > t) ]

Invalid input → Err:502

• Use EXPON.DIST for Poisson‑process waiting times
• Use CDF for probability questions
• Use PDF for density modeling
• Validate units (time, rate)
• Use RAND‑based inverse transform for simulation

• POISSON.DIST — event counts
• GAMMA.DIST — generalization of exponential
• WEIBULL.DIST — flexible lifetime modeling
• EXP — exponential function
• RAND — simulation

By mastering EXPON.DIST, you can build robust reliability, queueing, and stochastic models in LibreOffice Calc.