Data Analysis and Interpretation Flashcards

In a negative binomial regression model for claim counts, the dispersion parameter controls:

Answer: The mean-variance relationship, allowing variance to exceed the mean

The negative binomial dispersion parameter allows variance = mean + mean²/r, accommodating overdispersion relative to the Poisson (variance = mean).

A time series of monthly aggregate losses shows a significant spike every December. This pattern is best described as:

Answer: A seasonal component with period 12

Recurring patterns tied to calendar month represent seasonal variation; a December spike every year has a period of 12 months.

When comparing two predictive models using the Gini coefficient on a hold-out dataset, a higher Gini coefficient indicates:

Answer: Better rank-ordering discrimination between high- and low-risk policies

The Gini coefficient (derived from the Lorenz curve) measures how well a model separates high-risk from low-risk risks; higher Gini = better discrimination.

An actuary uses the Cape Cod method to estimate IBNR. Compared to the chain-ladder method, the Cape Cod method's primary advantage for immature accident years is:

Answer: It stabilizes estimates by using an empirical a priori loss ratio rather than relying solely on sparse reported data

The Cape Cod method derives the expected loss ratio from the data itself and applies it to unreported portions, reducing variance for immature years with little development.

A Lorenz curve is used in insurance to visualize how losses are distributed across a ranked population. The area between the Lorenz curve and the line of perfect equality is called the:

Answer: Gini index

The Gini index equals twice the area between the Lorenz curve and the 45-degree line of perfect equality.

For a loss severity model, the maximum likelihood estimator (MLE) of a lognormal distribution's parameters μ and σ² are:

Answer: The sample mean and sample variance of the log-transformed losses

For lognormal data, the MLE of μ is the sample mean of ln(X) and the MLE of σ² is the sample variance of ln(X) (divided by n, not n-1).

In a double-lift chart used to evaluate a predictive model, the y-axis represents cumulative loss ratio and the x-axis represents cumulative premium percentage ranked by predicted loss ratio. A well-performing model produces a curve that:

Answer: Lies above the diagonal for lower deciles and below for higher deciles

A good model places the worst-predicted risks first; their actual loss ratios are highest, so the lift curve rises steeply, then flattens — lying above the diagonal for low premium percentiles.