Society of Actuaries (SOA) PA Practice Exam

What distribution is usually recommended for a continuous positive target variable in GLMs?

1. Bernoulli

2. Normal

3. Gamma

4. Uniform

The correct answer is: Gamma

The gamma distribution is typically recommended for a continuous positive target variable in Generalized Linear Models (GLMs) due to its suitable properties for modeling positively skewed data. This distribution can handle variables that take only positive values, making it ideal for situations like modeling waiting times, insurance claims, and other scenarios where the response variable cannot logically take on negative values. The gamma distribution has two parameters, allowing for flexibility in shape, which enables it to appropriately model the variance of the data. In the context of GLMs, using the gamma distribution with a log link function helps in situations where the mean of the target variable is proportional to its variance, accommodating overdispersion often found in datasets. In contrast, other distributions mentioned have limitations. For instance, the Bernoulli distribution is suited for binary outcomes, the normal distribution assumes the data can take on negative values (which is inappropriate for continuous positive targets), and the uniform distribution is generally less suitable for capturing the characteristics of skewed data compared to the gamma distribution.