# least.squares: Finds the optimal Davies distribution for a dataset In Davies: The Davies Quantile Function

## Description

Finds the best-fit Davies distribution using either the least-squares criterion (`least.squares()`) or maximum likelihood (`maximum.likelihood()`)

## Usage

 ```1 2``` ```least.squares(data, do.print = FALSE, start.v = NULL) maximum.likelihood(data, do.print = FALSE, start.v = NULL) ```

## Arguments

 `data` dataset to be fitted `do.print` Boolean with `TRUE` meaning print a GFM `start.v` A suitable starting vector of parameters `c(C,lambda1,lambda2)`, with default `NULL` meaning to use `start()`

## Details

Uses `optim()` to find the best-fit Davies distribution to a set of data.

## Value

Returns the parameters C,lambda1,lambda2 of the best-fit Davies distribution to the dataset `data`

## Note

BUGS: can be screwed with bad value for `start.v`. Function `maximum.likelihod()` can be very slow. It might be possible to improve this by using some sort of hot-start for `optim()`.

## Author(s)

Robin K. S. Hankin

`davies.start`, `optim`, `objective`, `likelihood`
 ```1 2 3 4 5 6 7 8 9``` ```p <- c(10 , 0.1 , 0.1) d <- rdavies(50,p) system.time(print(maximum.likelihood(d))) #observe how long this takes. #The time is taken in repeated calls #to pdavies(), which uses uniroot(). system.time(print(least.squares(d))) #Much faster. ```