unifed.kappa {unifed} | R Documentation |
Cumulant generator of the unifed distribution
unifed.kappa(theta) unifed.kappa.prime(theta) unifed.kappa.double.prime(theta) unifed.kappa.prime.inverse(mu, ...) unifed.kappa.prime.inverse.one(mu, tol = 1e-07, maxit = 1e+07)
theta |
A numeric vector. |
mu |
A vector of numbers between 0 and 1 |
... |
Other parameters of |
tol |
Tolerance level. The algorithm stops if the proportional difference between the new and old value of an iteration is less or equal than this number. |
maxit |
Maximum number of iterations of the algorithm to look for convergence. |
The cumulant generator of the unifed distribution is defined as
/ | / theta \ | |e - 1| kappa(theta) = | log |----------| if theta ! = 0 | \ theta / | \ 0 if theta = 0
unifed.kappa.prime.inverse.one
uses the
Newthon-Raphson method for finding the inverse of
unifed.kappa.prime
for a single value.
unifed.kappa
returns a vector that contains the
cumulant generator of the unifed distribution applied to each
element of theta.
unifed.kappa.prime
returns a vector that contains
the derivative of the cumulant generator of the unifed
distribution for each element of theta.
unifed.kappa.double.prime
returns a vector that
contains the second derivative of the cumulant generator of the
unifed distribution for each element of theta.
unifed.kappa.prime.inverse
returns a vector with
unifed.kappa.prime.inverse.one
evaluated at every entry
of mu
.
unifed.kappa.prime.inverse.one
if the tolerance
level is reached within maxit
iterations, the function
returns the value of the last iteration. Otherwise it returns
NA
.
Quijano Xacur, Oscar Alberto (2018). The Unifed Distribution. ArXiv. http://arxiv.org/abs/1812.00251.
Jørgensen, Bent (1997). The Theory of Dispersion Models. Chapman & Hall, London.
unifed.kappa(1) unifed.kappa(-5:5) unifed.kappa.prime(4.5) unifed.kappa.double.prime(0) unifed.kappa.prime.inverse(0.5) unifed.kappa.prime.inverse(c(0.1,0.7,0.9))