# dist-hypFit: Fit of a Hyperbolic Distribution In fBasics: Rmetrics - Markets and Basic Statistics

## Description

Estimates the parameters of a hyperbolic distribution.

## Usage

 ```1 2 3 4``` ``` 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

 ```1 2 3 4 5 6 7 8 9``` ``` ## 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 March 13, 2020, 9:09 a.m.