# Find Starting Values for Fittting a 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 |

`startValues` |
Code giving the method of determining starting values for finding the maximum likelihood estimates of the parameters. |

`paramStart` |
If |

### 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 |

`breaks` |
The cell boundaries found by a call to |

`midpoints` |
The cell midpoints found by a call to |

`empDens` |
The estimated density at the midpoints found by a call
to |

`svName` |
Name of the method used to find the starting values. |

### Author(s)

David Scott d.scott@auckland.ac.nz, 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.

### See Also

`hist`

, `density`

, `dskewhyp`

,
`skewhypFit`

, `skewhypCheckPars`

### Examples

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
``` |

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