Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# The Gamma Distribution¤

The gamma distribution generalises the exponential distribution. It can be regarded as the time to the Nth failure if the time to failure is exponentially distributed.

The probability density function of the gamma distribution is:

f(t) = if t 0 and zero otherwise. Here is the gamma function (see The Summary of the Gamma Function screen in the previous session).

When N = 1, then we get the exponential distribution f(t) = . However N does not have to be an integer. The mean is and the standard deviation is . The effects of changing lambda and N can be seen in these graphs of f(t), but you can click on them for an interactive version in Excel where you can experiment with different values yourself.