Investment Studio > Expressions > Functions > Statistical > EXPONDIST
float expondist(float x, float lambda, boolean cumulative = TRUE)
Returns the value at x >= 0 of the exponential probability function with coefficient lambda >= 0.
If cumulative = TRUE, the CDF (Cumulative Distribution Function) is returned (equal to the probability that x is >= a stochastic variable with exponential distribution); otherwise, the PDF (Probability Density Function) is returned. If cumulative is omitted, it defaults to TRUE.
Mathematically, the exponential PDF is
f(x, l) = l e-l x
and the CDF is
| x | ||
| F(x, l) = | ó | f(u, l) du = 1 - e-l x |
| ô | ||
| õ | ||
| 0 |
The exponential PDF can be proved to be the only memory-less random distribution. It therefore describes the distribution of time intervals between any kind of independent, random events with mean waiting time = 1 / l. It is therefore customary to call l the "intensity" (= events / time unit).
Example
If a piece of radioactive material undergoes (on average) l = 120 decays an hour, the probability of the time left till the next decay being <= one minute is
=expondist(1 / 60, 120)
» 86.47%.