The Malthusian parameter for Green's model of asymmetric budding

Let denote the (random) cell generation time for mother cells and denote the extra time for daughter cells. The Malthusian parameter is the unique positive root of the equation

If the random variable has mean and variance and the random variable has mean and variance , a simple approximation to the Malthusian parameter that is usually extremely accurate is

where

is the average of the generation times for mother and daughter cells.