Gamma Regression

Consider a continuous dependent variable that is positive-valued, such as a length of a hospital stay, time waiting or the cost of a bill. This type of data is continuous in nature and oftentimes skewed and a normal approximation does not hold.

The type of data above presents a constant Coefficient of Variation (CV), that is:

$$ \sqrt{var(Y_i)} \over E(Y_i) = \sigma $$

The identity induces a quadratic variance function:

$$ var(Y_i) = \sigma^2E(Y_i)^2 $$