R: Parameter Fit of a Distribution

DistributionFits {fBasics}

R Documentation

Parameter Fit of a Distribution

Description

A collection and description of moment and maximum likelihood estimators to fit the parameters of a distribution.

The functions are:

`nFit`	MLE parameter fit for a normal distribution,
`tFit`	MLE parameter fit for a Student t-distribution,
`stableFit`	MLE and Quantile Method stable parameter fit.

Usage

nFit(x, doplot = TRUE, span = "auto", title = NULL, description = NULL, ...)

tFit(x, df = 4, doplot = TRUE, span = "auto", trace = FALSE, title = NULL, 
    description = NULL, ...)
    
stableFit(x, alpha = 1.75, beta = 0, gamma = 1, delta = 0, 
    type = c("q", "mle"), doplot = TRUE, control = list(),
    trace = FALSE, title = NULL, description = NULL) 
    
## S4 method for signature 'fDISTFIT'
show(object)

Arguments

`control`	[stableFit] - a list of control parameters, see function `nlminb`.
`alpha, beta, gamma, delta`	[stable] - The parameters are `alpha`, `beta`, `gamma`, and `delta`: value of the index parameter `alpha` with `alpha = (0,2]`; skewness parameter `beta`, in the range [-1, 1]; scale parameter `gamma`; and shift parameter `delta`.
`description`	a character string which allows for a brief description.
`df`	the number of degrees of freedom for the Student distribution, `df > 2`, maybe non-integer. By default a value of 4 is assumed.
`object`	[show] - an S4 class object as returned from the fitting functions.
`doplot`	a logical flag. Should a plot be displayed?
`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?
`type`	a character string which allows to select the method for parameter estimation: `"mle"`, the maximum log likelihood approach, or `"qm"`, McCulloch's quantile method.
`x`	a numeric vector.
`...`	parameters to be parsed.

Details

Stable Parameter Estimation:

Estimation techniques based on the quantiles of an empirical sample were first suggested by Fama and Roll [1971]. However their technique was limited to symmetric distributions and suffered from a small asymptotic bias. McCulloch [1986] developed a technique that uses five quantiles from a sample to estimate alpha and beta without asymptotic bias. Unfortunately, the estimators provided by McCulloch have restriction alpha>0.6.

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.
`gradient`	the gradient at the estimated maximum.

Remark: The parameter estimation for the stable distribution via the maximum Log-Likelihood approach may take a quite long time.

Examples

    
## nFit -
   # Simulate random normal variates N(0.5, 2.0):
   set.seed(1953)
   s = rnorm(n = 1000, 0.5, 2) 

## nigFit -  
   # Fit Parameters:
   nFit(s, doplot = TRUE)

[Package fBasics version 2160.81 Index]