Description Usage Arguments Details Value Examples
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. 
1 2 3 4 5 6 7 8 9 10 11  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)

control 
[stableFit]  
alpha, beta, gamma, delta 
[stable]  
description 
a character string which allows for a brief description. 
df 
the number of degrees of freedom for the Student distribution,

object 
[show]  
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 
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: 
x 
a numeric vector. 
... 
parameters to be parsed. 
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
.
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 LogLikelihood approach may take a quite long time.
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