first things first: I am not a studied mathematician and therefore lack thorough knowledge of the topic - please consider this, even though I will of course try to express myself as accurately as possible.
I want to calculate a continuous random variable $A$, which represents a specific amount of time following a to me unknown distribution. It is calculated by a formula that itself contains 4 other random variables $B, C, D$ and $E$, which can either be deterministicially (i.e. they always take the same fixed value) or exponentially distributed. Additionally, there is a constant factor $x$ involved. The formula for calculating $A$ is:
$A = B + max(\frac{C}{E}, x*\frac{D}{E})$
I need to use this distribution in another program. As it is probably not possible to use one of the 'standard' distributions for it, I stumbled upon this paragraph in the program's manual
Empirical distributions are supported in the following way. The user is ex- pected to provide a probability distribution function (PDF), specified as an array of positive real numbers (histogram). The array is read from an external text file whose name and location are initialized using the "Input File" parameter. Successive values in the text file must be delimited using semicolon ';' characters. A cumulative distribution function (CDF) is constructed from the PDF and inverted using a binary search for the nearest bin boundary and a linear interpolation within the bin (resulting in a constant density within each bin).
So, how would I be able to provide these bins for $A$ ?
Do i need to generate random numbers which follow its distribution and then somehow calculate the bins?
Please help or ask any questions if I did not explain something correctly.
Kind regards and thanks in advance!