kappa4Int: Arc length of four-parameter kappa CDF.
In mtloots/alR: Arc Lengths of Statistical Functions

Description Usage Arguments Details Value Examples

Calculate the arc length for a univariate four-parameter kappa cumulative distribution function over a specified interval.

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kappa4Int(mu, sigma, h, k, tau, q1, q2, quantile)

kappa4Int2(mu, sigma, h, k, tau, q1, q2, quantile)

`mu`	A real number specifying the location parameter.
`sigma`	A positive real number specifying the scale parameter.
`h, k`	Real numbers specifying the two shape parameters.
`tau`	A real number between 0 and 1, corresponding to the CDF value at the point of truncation.
`q1`	The point (or vector for `kappa4Int2`) specifying the lower limit of the arc length integral.
`q2`	The point (or vector for `kappa4Int2`) specifying the upper limit of the arc length integral.
`quantile`	Logical, TRUE/FALSE, whether `q1` and `q2` are quantiles, or actual points in the domain.

The arc length of a univariate four-parameter kappa cumulative distribution function is approximated using the numerical integration C code implimented for R's integrate functions, i.e. using Rdqags. For this approximation, subdiv = 100 (100 subdivisions), and eps_abs = eps_rel = 1e-10, i.e. the absolute and relative errors respectively.

kappa4Int: A list with the following components:

value: The resultant arc length.
abs.err: The absolute error between iterations. subdivisions: Number of subdivisions used in the numerical approximation.
neval: Number of function evaluations used by the numerical approximation.

kappa4Int2: A vector having length equal to that of the vector of lower quantile bounds, containing the arc lengths requested for a four-parameter kappa cumulative distribution function.

library(alR)
mu <- 4
sigma <- 0.4
h <- -4
tau <- 1 ## no truncation
k <- kappa4tc(-4, 0, 1)$par
kappa4Int(mu, sigma, h, k, tau, 0.025, 0.975, TRUE)
p1 <- qkappa4(0.025, mu, sigma, h, k)
p2 <- qkappa4(0.975, mu, sigma, h, k)
kappa4Int(mu, sigma, h, k, tau, p1, p2, FALSE)

kappa4Int2(mu, sigma, h, k, tau, c(0.025, 0.5), c(0.5, 0.975), TRUE)
p12 <- qkappa4(0.5, mu, sigma, h, k)
kappa4Int2(mu, sigma, h, k, tau, c(p1, p12), c(p12, p2), FALSE)