The Exponential distribution is a distribution concentrated on the set of positive numbers. The distribution is particularly well suited to model uncertainty of quantities being a minimum of many 窶忖nderlying窶 variables. The Exponential distribution is often used to model uncertainty about variables representing duration. Especially it is popular as a lifetime distribution in reliability applications.
In the Exponential distribution the key numbers, 窶彗窶, 窶彙窶 and 窶彡窶 are interpreted as follows:
窶彗窶 = The 10%-fractile.
窶彙窶 = The 50%-fractile.
窶彡窶 = The 90%-fractile.
To get a sensible distribution, the specified values must satisfy:
0 < 窶彗窶 < 窶彙窶 < 窶彡窶
DynRisk will adjust the numbers further to make the fractiles fit the fractiles of an exponential distribution.
In many applications it is more usual to specify Exponential distribution by specifying the 窶徼ransition rate窶 of the distribution. (In reliability applications the transition rate is usually called the 窶彷ailure rate窶.) To specify an Exponential distribution with transition rate say L, you can calculate the corresponding key numbers using the following:
