Iterative Koutrouvelis regression method with different spacing schemes (points where the eCF is computed).
1 2 3  KoutParametersEstim(x, theta0 = NULL,
spacing = c("Kout", "UniformSpac", "ArithSpac", "free"),
pm = 0, tol = 0.05, NbIter = 10, PrintTime = FALSE, ...)

x 
Data used to perform the estimation: vector of length n. 
theta0 
Initial guess for the 4 parameters values: vector of length 4 
spacing 
Scheme used to select the points where the moment conditions are
evaluated. 
pm 
Parametrisation, an integer (0 or 1); default: 
tol 
The loop stops if the relative error between two
consecutive estimation is smaller then

NbIter 
Maximum number of iteration. The loop stops when 
PrintTime 
Logical flag; if set to TRUE, the estimation duration is printed out to the screen in a readable format (h/min/sec). 
... 
Other arguments to pass to the function. See details 
spacing 4 options for the spacing scheme are implemented as described above. In particular:
UniformSpac
, ArithSpac
:user can specify the
number of points to choose in both regression by inputting
nb_t
and nb_u
. Otherwise the Koutrouvelis table will be
used to compte them.
free
:User is expected to provide t_points
and u_points
otherwise the Kout
scheme will be used.
Returns a list with the following elements:
Estim 

duration 
estimation duration in a numerical format 
method 

Koutrouvelis IA (1980). “Regressiontype estimation of the parameters of stable laws.” Journal of the American Statistical Association, 75(372), pp. 918–928.
Koutrouvelis IA (1981). “An iterative procedure for the estimation of the parameters of stable laws: An iterative procedure for the estimation.” Communications in StatisticsSimulation and Computation, 10(1), pp. 17–28.
Estim
1 2 3 4 5 6 7 8  pm=0
theta < c(1.45,0.5,1.1,0.4)
set.seed(1235);x < rstable(200,theta[1],theta[2],theta[3],theta[4],pm=pm)
theta0=theta0.1
spacing="Kout"
KoutParametersEstim(x=x,theta0=theta0,
spacing=spacing,pm=pm)

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