# skewhypFitStart: Find Starting Values for Fittting a Skew Hyperbolic Student... In SkewHyperbolic: The Skew Hyperbolic Student t-Distribution

## Description

Finds starting values for input to a maximum likelihood routine for fitting a skew hyperbolic t-distribution to data.

## Usage

 ```1 2``` ```skewhypFitStart(x, breaks = NULL, startValues = "LA", paramStart = NULL) skewhypFitStartLA(x, breaks = NULL) ```

## Arguments

 `x` Data vector. `breaks` Breaks for histogram. If missing defaults to those generated by `hist(x, right = FALSE, plot =FALSE)`. If `startValues = "LA"` then 30 breaks are used by default. `startValues` Code giving the method of determining starting values for finding the maximum likelihood estimates of the parameters. `paramStart` If `startValues = "US"` the user must specify a vector of starting parameter values in the form `c(mu,log(delta),beta,log(nu))`.

## Details

`startValues` can be either `"US"`(User-supplied) or `"LA"` (Linear approximation).

If `startValues = "US"` then a value for `paramStart` must be supplied. The parameters are checked for validity by the function `skewhypCheckPars`.

If `startValues = "LA"` a linear approximation is made to the log-density in each of the tails, from which the estimates for nu and beta are found. The remaining two parameters, delta and mu are found by solving the moment equations for mean and variance. Since the variance does not exist for values of nu <= 4, the estimate of nu will be at least 4.1. Note that if the distribution is too skewed, there are not enough points in the lighter tail to fit the required linear model, and the method will stop and return a warning. User supplied values will have to be used in this case.

## Value

`skewhypFitStart` returns a list with components:

 `paramStart` A vector of the form `c(mu,delta,beta,nu)` giving the generated starting values of the parameters. `breaks` The cell boundaries found by a call to `hist`. `midpoints` The cell midpoints found by a call to `hist`. `empDens` The estimated density at the midpoints found by a call to `hist` if `startValues = "US"` or `density` if `startValues = "LA"`. `svName` Name of the method used to find the starting values.

## Author(s)

David Scott [email protected], Fiona Grimson

## References

Aas, K. and Haff, I. H. (2006). The Generalised Hyperbolic Skew Student's t-distribution, Journal of Financial Econometrics, 4, 275–309.

`hist`, `density`, `dskewhyp`, `skewhypFit`, `skewhypCheckPars`
 ```1 2 3 4 5 6``` ```## find starting values to feed to skewhypFit data(lrnokeur) skewhypFitStart(lrnokeur, startValues="LA")\$paramStart ## user supplied values skewhypFitStart(lrnokeur, startValues="US", paramStart=c(0,0.01,0,5))\$paramStart ```