Description
Usage
Arguments
Details
Value
Examples
Estimates the parameters of a hyperbolic distribution.

(x, alpha = 1, = 0, delta = 1, mu = 0,
= , doplot = , span = "auto", = ,
= , description = , )

alpha, beta, delta, mu 
alpha is a shape parameter by default 1,
beta is a skewness parameter by default 0,
note abs(beta) is in the range (0, alpha),
delta is a scale parameter by default 1,
note, delta must be zero or positive, and
mu is a location parameter, by default 0.
These is the meaning of the parameters in the first
parameterization pm=1 which is the default
parameterization selection.
In the second parameterization, pm=2 alpha
and beta take the meaning of the shape parameters
(usually named) zeta and rho .
In the third parameterization, pm=3 alpha
and beta take the meaning of the shape parameters
(usually named) xi and chi .
In the fourth parameterization, pm=4 alpha
and beta take the meaning of the shape parameters
(usually named) a.bar and b.bar .

description 
a character string which allows for a brief description.

doplot 
a logical flag. Should a plot be displayed?

scale 
a logical flag, by default TRUE . Should the time series
be scaled by its standard deviation to achieve a more stable
optimization?

span 
xcoordinates for the plot, by default 100 values
automatically selected and ranging between the 0.001,
and 0.999 quantiles. Alternatively, you can specify
the range by an expression like span=seq(min, max,
times = n) , where, min and max are the
left and right endpoints of the range, and n gives
the number of the intermediate points.

title 
a character string which allows for a project title.

trace 
a logical flag. Should the parameter estimation process be
traced?

x 
a numeric vector.

... 
parameters to be parsed.

The function nlm
is used to minimize the "negative"
maximum loglikelihood function. nlm
carries out a minimization
using a Newtontype algorithm.
The functions tFit
, hypFit
and nigFit
return
a list with the following components:
estimate 
the point at which the maximum value of the log liklihood
function is obtained.

minimum 
the value of the estimated maximum, i.e. the value of the
log liklihood function.

code 
an integer indicating why the optimization process terminated.
1: relative gradient is close to zero, current iterate is probably
solution;
2: successive iterates within tolerance, current iterate is probably
solution;
3: last global step failed to locate a point lower than estimate .
Either estimate is an approximate local minimum of the
function or steptol is too small;
4: iteration limit exceeded;
5: maximum step size stepmax exceeded five consecutive times.
Either the function is unbounded below, becomes asymptotic to a
finite value from above in some direction or stepmax
is too small.

gradient 
the gradient at the estimated maximum.

steps 
number of function calls.


## rhyp 
# Simulate Random Variates:
(1953)
s = (n = 1000, alpha = 1.5, = 0.3, delta = 0.5, mu = 1.0)
## hypFit 
# Fit Parameters:
(s, alpha = 1, = 0, delta = 1, mu = (s), doplot = )

fBasics documentation built on March 13, 2020, 9:09 a.m.