Fit normal, Student-t and stable distributions — DistributionFits • fBasics

A collection 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)

Arguments

x

a numeric vector.

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.

control

a list of control parameters, see function nlminb.

alpha, beta, gamma, delta

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.

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.

...

parameters to be parsed.

Value

an object from class "fDISTFIT".

Slot fit has components estimate, minimum, code and gradient (but for nFit code is NA and gradient is missing).

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.

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

Examples

set.seed(1953)
s <- rnorm(n = 1000, 0.5, 2) 

nFit(s, doplot = TRUE) 

#> 
#> Title:
#>  Normal Parameter Estimation 
#> 
#> Call:
#>  nFit(x = s, doplot = TRUE)
#> 
#> Model:
#>  Normal Distribution
#> 
#> Estimated Parameter(s):
#>      mean        sd 
#> 0.4952318 2.0767958 
#>