The Binary distribution is concentrated in just two points. In most applications the Binary distribution as an 窶彿ndicator窶 variable for a certain event. That is, the variable is either 0 or 1, and it is 1 if and only if the corresponding event actually occurs.
Assume e.g., that a certain project cost, K, contributes to the total cost only if an event E occurs. E may for instance be a certain accidental event. In other words, if E occurs, one has to pay the cost K, while if E does not occur, then K can be neglected.
Now, let X be 1 if E occurs and 0 otherwise. Assume that the probability of E is assessed to be p, some number between 0 and 1. The cost K itself may have a suitable lognormal distribution. The experienced cost may then be expressed as:
Experienced cost = H = X * K
Note that even though K is lognormally distributed, H is not. In fact there is a positive probability of (1-p) that H is exactly 0.
In the Binary distribution the key numbers, 窶彗窶, 窶彙窶 and 窶彡窶 are interpreted as follows:
窶彗窶 = Min. of two possible values.
窶彙窶 = The expected value.
窶彡窶 = Max. of two possible values.
To get a sensible distribution the specified values must satisfy:
窶彗窶 竕､ 窶彙窶 竕､ 窶彡窶
If the key numbers are not ordered according to these rules, DynRisk will reorder them before doing any calculations.
Note! In the case of indicator variables, i.e., where 窶彗窶 is 0 and 窶彡窶 is 1, then the expected value is equal to the probability of getting the outcome 窶1窶. Thus, in such cases it is fairly easy to specify the expectation, i.e., the 窶彙窶 parameter. In the general case where the 窶彗窶 and the 窶彡窶 values are say A and C respectively, and the probability of the value C is assessed to be, say p, the expectation is given by the following formula:
Expectation = 窶彙窶 = A(1-p) + Cp
Since p is always a number between 0 and 1, it follows that 窶彙窶 always should be a number between 窶彗窶 and 窶彡窶. Especially, if p is close to 1, then 窶彙窶 is close to 窶彡窶, while if p is close to 0, then 窶彙窶 is close to 窶彗窶.
If we are given the values of 窶彗窶, 窶彡窶 and the expectation, 窶彙窶, say A, C and B respectively, we can calculate the corresponding probability, p of getting the 窶彡窶 value using the following formula:
