# hyperbFitStart: Find Starting Values for Fitting a Hyperbolic Distribution In HyperbolicDist: The Hyperbolic Distribution

 hyperbFitStart R Documentation

## Find Starting Values for Fitting a Hyperbolic Distribution

### Description

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

### Usage

``````  hyperbFitStart(x, breaks = NULL, startValues = "BN",
ThetaStart = NULL, startMethodSL = "Nelder-Mead",
``````

### Arguments

 `x` Data vector. `breaks` Breaks for histogram. If missing, defaults to those generated by `hist(x, right = FALSE, plot = FALSE)`. `startValues` Vector of the different starting values to consider. See Details. `ThetaStart` Starting values for Theta if ```startValues = "US"```. `startMethodSL` Method used by call to `optim` in finding skew Laplace estimates. `startMethodMoM` Method used by call to `optim` in finding method of moments estimates. `...` Passes arguments to `optim`.

### Details

Possible values of the argument `startValues` are the following:

`"US"`

User-supplied.

`"BN"`

Based on Barndorff-Nielsen (1977).

`"FN"`

A fitted normal distribution.

`"SL"`

Based on a fitted skew-Laplace distribution.

`"MoM"`

Method of moments.

If `startValues = "US"` then a value must be supplied for `ThetaStart`.

If `startValues = "MoM"`, `hyperbFitStartMoM` is called. These starting values are based on Barndorff-Nielsen et al (1985).

If `startValues = "SL"`, or `startValues = "MoM"` an initial optimisation is needed to find the starting values. These optimisations call `optim`.

### Value

`hyperbFitStart` returns a list with components:

 `ThetaStart` A vector with elements `pi`, `lZeta` (log of zeta), `lDelta` (log of delta), and `mu` giving the starting value of Theta. `xName` A character string with the actual `x` argument name. `breaks` The cell boundaries found by a call to `hist`. `midpoints` The cell midpoints found by a call to `hist`. `empDens` The estimated density found by a call to `hist`.

`hyperbFitStartMoM` returns only the method of moments estimates as a vector with elements `pi`, `lZeta` (log of zeta), `lDelta` (log of delta), and `mu`.

### Author(s)

David Scott d.scott@auckland.ac.nz, Ai-Wei Lee, Jennifer Tso, Richard Trendall, Thomas Tran

### References

Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401–419.

Barndorff-Nielsen, O., Blæsild, P., Jensen, J., and Sörenson, M. (1985). The fascination of sand. In A celebration of statistics, The ISI Centenary Volume, eds., Atkinson, A. C. and Fienberg, S. E., pp. 57–87. New York: Springer-Verlag.

Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.

`HyperbolicDistribution`, `dskewlap`, `hyperbFit`, `hist`, and `optim`.

### Examples

``````Theta <- c(2,2,2,2)
dataVector <- rhyperb(500,Theta)
hyperbFitStart(dataVector,startValues="FN")
hyperbFitStartMoM(dataVector)
hyperbFitStart(dataVector,startValues="MoM")
``````

HyperbolicDist documentation built on Nov. 26, 2023, 9:07 a.m.