Statistical
Exponential Distribution PDF, CDF, and Memoryless Survival Probability (EXPON.DIST Formula)
Calculate inter-arrival probability density, cumulative failure probability, survival probability P(T > x), and target SLA quantiles using EXP and LN.
Exact closed-form exponential distribution formulas
For an arrival or failure process occurring at constant rate lambda > 0 events per unit time (mean wait 1 / lambda), Excel's EXPON.DIST(x, lambda, FALSE) evaluates the density f(x) = lambda * EXP(-lambda * x), while EXPON.DIST(x, lambda, TRUE) evaluates the cumulative probability F(x) = 1 - EXP(-lambda * x).
Its complement EXP(-lambda * x) gives the survival probability P(T > x) that zero events occur within window x, and inverting F(x) = p gives the exact percentile wait time x_p = -LN(1 - p) / lambda.
| Rate (lambda) | Time Window (x) | CDF 1 - e^(-lx) | PDF l * e^(-lx) | Survival e^(-lx) |
|---|---|---|---|---|
| 0.25 / min (mean 4m) | 4.0 min | 0.632121 | 0.091970 | 0.367879 |
| 0.25 / min (mean 4m) | 8.0 min | 0.864665 | 0.033834 | 0.135335 |
| 0.25 / min (mean 4m) | 0.0 min | 0.000000 | 0.250000 | 1.000000 |
| Median Wait (p = 0.50) | 2.7726 min | 0.500000 | 0.125000 | 0.500000 |
Exponential Cumulative Probability Formula (EXPON.DIST Cumulative)
Computes F(x) = 1 - EXP(-lambda * x) for rate B2 and elapsed time B3, guarding negative x or non-positive lambda.
=IF(OR(B2 <= 0, B3 < 0), "#NUM!", ROUND(1 - EXP(-B2 * B3), 6))Exponential Density (PDF) & Percentile Quantile Formula
Evaluates f(x) = lambda * EXP(-lambda * x) for density curves, or -LN(1 - B4) / B2 to solve for the time threshold corresponding to cumulative probability B4.
=ROUND(-LN(1 - B4) / B2, 4)Try the example
Use the original values or change them to test your understanding.