# Distribution Functions - DistProb, DistValue, DistTransProb

DistProb(Distribution, Value) --> Cum Probability

This function accepts a distribution and a value within the range of samples for that distribution, and it returns the probability of the distribution returning a sample less than or equal to that value.

For example, if you enter a normal distribution (symmetrical) and the mean of that distribution, DistProb will return 0.5 because there is a 50% likelihood that a sample would be less than or equal to the mean.

DistValue(Distribution, cum_prob) --> Value

This function accepts a distribution and a cum probability and returns the value at that point in the cumulative density function (CDF) based on the cumulative probability provided.

For example, if you enter a normal distribution (symmetrical) and 0.5 as the cumulative probability, DistValue will return the distribution mean because the mean is exactly half way through the CDF.

DistTransProb(Distribution, cycle_start, cycle_length) --> Probability

Use this when you are converting DES time-to-event distributions to Markov transition probabilities.

This function accepts a distribution, a start time and an interval length and returns the probability of the event occurring during that cycle. This function should only be used for distributions that represent a time-to-event.

For example, if you enter an exponential distribution, any start time, and a cycle length of 1, you should always get the same probability since the exponential distribution has fixed risk.

There is an example model attached to try to demonstrate the use of these functions and show the relationship among the functions.