PiecewisePareto_CDF {Pareto}

Distribution Function of the Piecewise Pareto Distribution

Description

Calculates the cumulative distribution function of a Piecewise Pareto Distribution. This function is deprecated. Use pPiecewisePareto instead.

Usage

PiecewisePareto_CDF(x, t, alpha, truncation = NULL, truncation_type = "lp")

Arguments

x

Numeric. The function evaluates the CDF at x.

t

Numeric vector. Thresholds of the piecewise Pareto distribution.

alpha

Numeric vector. alpha[i] is the Pareto alpha in excess of t[i].

truncation

Numeric. If truncation is not NULL and truncation > t, then the distribution is truncated at truncation.

truncation_type

Character. If truncation_type = "wd" then the whole distribution is truncated. If truncation_type = "lp" then a truncated Pareto is used for the last piece.

Value

Distribution function of the piecewise Pareto distribution with parameter vectors t and alpha evaluated at x

References

Riegel, U. (2018) Matching tower information with piecewise Pareto. European Actuarial Journal 8(2): 437–460

Examples

t <- c(1000, 2000, 3000)
alpha <- c(1, 1.5, 2)
x <- 0:10 * 1000
pPiecewisePareto(x, t, alpha)
pPiecewisePareto(x, t, alpha, truncation = 5000, truncation_type = "lp")
pPiecewisePareto(x, t, alpha, truncation = 5000, truncation_type = "wd")