dist-hypFit: Fit a Hyperbolic distribution

In fBasics: Rmetrics - Markets and Basic Statistics

Fit 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

x	a numeric vector.
alpha	shape parameter, a positive number.
beta	skewness parameter, abs(beta) is in the range (0, alpha).
delta	scale parameter, must be zero or positive.
mu	location parameter, by default 0.
scale	a logical flag, by default TRUE. Should the time series be scaled by its standard deviation to achieve a more stable optimization?
doplot	a logical flag. Should a plot be displayed?
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.
trace	a logical flag. Should the parameter estimation process be traced?
title	a character string which allows for a project title.
description	a character string which allows for a brief description.
...	parameters to be parsed.

Details

The meaning of the parameters given above corresponds to the first parameterization, see dhyp for 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

an object from class "fDISTFIT". Slot fit is 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) 

fBasics documentation built on Nov. 3, 2023, 5:10 p.m.