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

The functions are:

nFitMLE parameter fit for a normal distribution,
tFitMLE parameter fit for a Student t-distribution,
stableFitMLE and Quantile Method stable parameter fit.


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)



a numeric vector.


a logical flag. Should a plot be displayed?


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.


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.


a character string which allows for a brief description.


the number of degrees of freedom for the Student distribution, df > 2, maybe non-integer. By default a value of 4 is assumed.


a character string which allows for a project title.


a logical flag. Should the parameter estimation process be traced?


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.


an object from class "fDISTFIT"


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.


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

## nigFit -  
   # Fit Parameters:
   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