R: Fit of a Hyperbolic Distribution

hypFit {fBasics}

R Documentation

Fit of a Hyperbolic Distribution

Description

Estimates the parameters of a hyperbolic distribution.

Usage

    
hypFit(x, alpha = 1, beta = 0, delta = 1, mu = 0, 
    scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE, 
    title = NULL, description = NULL, ...)

Arguments

`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`	x-coordinates 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.

Details

The function nlm is used to minimize the "negative" maximum log-likelihood function. nlm carries out a minimization using a Newton-type algorithm.

Value

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.

Examples

    
## rhyp -
   # Simulate Random Variates:
   set.seed(1953)
   s = rhyp(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0) 

## hypFit -  
   # Fit Parameters:
   hypFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)

[Package fBasics version 2160.81 Index]