Parametric fit of a distribution
distDistributionFits.Rd
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 tdistribution, 
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
xcoordinates 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
andmax
are the left and right endpoints of the range, andn
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
, anddelta
:
value of the index parameteralpha
withalpha = (0,2]
; skewness parameterbeta
, in the range [1, 1]; scale parametergamma
; and shift parameterdelta
.  description
a character string which allows for a brief description.
 df
the number of degrees of freedom for the Student distribution,
df > 2
, maybe noninteger. 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.
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 LogLikelihood 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)
#>
#> Title:
#> Normal Parameter Estimation
#>
#> Call:
#> nFit(x = s, doplot = TRUE)
#>
#> Model:
#> Normal Distribution
#>
#> Estimated Parameter(s):
#> mean sd
#> 0.4952318 2.0767958
#>