Specify an individual claim severity distribution

Creates a lightweight specification of a nonnegative claim amount \(X\). A specification records the probabilistic model; it does not fit data, draw samples, discretize amounts, or calculate aggregate losses.

Usage

severity_spec(dist, ..., custom = NULL, label = NULL)

Arguments

dist: One of "exponential", "gamma", "lognormal", "weibull", "pareto", "burr", "loglogistic", "degenerate", "discrete", or "custom".
...: Named distribution parameters, as described in Details.
custom: Named list of computational functions and support information when dist = "custom"; NULL for built-in families.
label: Optional nonempty character scalar identifying the model.

Value

An object with classes "tidyact_severity_spec" and "tidyact_distribution_spec". The ordered fields are schema_version, dist, params, support, data, custom, label, and metadata. Its data field is NULL; empirical severities are handled separately.

Details

All severities satisfy \(X \ge 0\). The supported built-in models are:

Exponential: rate > 0, matching stats::dexp().
Gamma: shape > 0, rate > 0, matching stats::dgamma().
Lognormal: meanlog is finite and sdlog > 0, matching stats::dlnorm(). A point mass is specified with "degenerate".
Weibull: shape > 0, scale > 0, matching stats::dweibull().
Pareto II (Lomax): shape > 0, scale > 0; the survival function is \(P(X>x)=(1+x/\mathrm{scale})^{-\mathrm{shape}}\) for \(x \ge 0\). This is not the Pareto I distribution with positive lower endpoint.
Burr XII: shape1 > 0, shape2 > 0, scale > 0, with survival function \(P(X>x)=[1+(x/\mathrm{scale})^{\mathrm{shape1}}]^{-\mathrm{shape2}}\).
Log-logistic: shape > 0, scale > 0, the Burr XII special case shape1 = shape, shape2 = 1.
Degenerate: value >= 0 is a finite amount with probability one.
Finite discrete: values is a strictly increasing vector of distinct finite nonnegative amounts; probs contains strictly positive probabilities, with the same length and summing to one (to numerical tolerance). Amounts need not be integer multiples of a common unit.

Unlike a frequency distribution, an individual claim severity may have an atom at zero and need not be absolutely continuous. The "degenerate" and "discrete" models are represented as discrete specifications rather than being forced into a continuous family.

For dist = "custom", custom must be a named list with support and at least one of pdf or pmf. The support list must contain type, lower, and upper, with type in "continuous", "discrete", "lattice", or "mixed"; lattice support additionally requires a positive step. The support component may also be a function of params returning that list. A mixed specification requires pdf, pmf, and cdf. Custom operations, when provided, follow these interfaces: pdf(x, params, log = FALSE), pmf(x, params, log = FALSE), cdf(q, params, lower.tail = TRUE, log.p = FALSE), quantile(p, params, lower.tail = TRUE, log.p = FALSE), rng(n, params), raw_moment(order, params), limited_moment(order, limit, params), mgf(t, params), and laplace(t, params). The argument params is the named list collected from .... As with frequency_spec(), the constructor checks the shape of a custom definition but cannot certify its mathematical validity.

The internal registry supplies probability functions and raw moments for built-in families. Some advanced operations (for example limited moments, the MGF of heavy-tailed distributions, and numerical Laplace transforms) are intentionally left unavailable until their public interfaces are set. In particular, no numerical approximation is performed by this constructor.

References

Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., and Nesbitt, C. J. (1997). Actuarial Mathematics, 2nd ed. Society of Actuaries.

Examples