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A collection of methods to estimate parameters of different temperedstable distributions. Currently, there are seven different temperedstable distributions to choose from: Tempered stable subordinatordistribution, classical tempered stable distribution (TSD), normal TSD,generalized classical TSD, modified TSD, Kim-Rachev TSD, rapidlydecreasing TSD. The package also provides functions to compute densityand probability functions and tools to run Monte Carlo simulations.

The main function of this package are briefly described below:

• Main function: TemperedEstim() computes all the information about theestimator. It allows the user to choose the preferred method andseveral related options.
• Characteristic function, density function, probability function andother functions for every tempered stable distribution mentionedabove. E.g. charTSS(), dCTS(), …
• Monte Carlo simulation: a tool to run a Monte Carlo simulation(TemperedEstim_Simulation()) is provided and can save output files orproduce statistical summary.

The package was developed by Till Massing and Cedric Jüssen and isstructurally based on the “StableEstim” package by Tarak Kharrat andGeorgi N. Boshnakov.

Since we use the package “copula” and this uses C code, it may be thatthis package has to be installed manually beforehand.

TempStable is now available on CRAN! In R-Studio the package can beinstalled directly with the following command:

install.packages("TempStable")

You can install the development version of TempStable fromGitHub with:

# install.packages("devtools")devtools::install_github("TMoek/TempStable")

This is a basic example which shows you how to solve a common problem:

library(TempStable)## basic example code# Such a simulation can take a very long time. Therefore, it can make sense to# parallelise after Monte Carlo runs. Parallelisation of the simulation is not# yet part of the package.# For testing purposes, the amount of runs and parameters is greatly reduced.# Therefore, the result is not meaningful. To start a meaningful simulation, the# SampleSize could be, for example, 1000 and MCParam also 1000.thetaT<- c(1.5,1,1,1,1,0)res_CTS_ML_size10<- TemperedEstim_Simulation(ParameterMatrix= rbind(thetaT),SampleSizes= c(10),MCparam=3,TemperedType="CTS",Estimfct="ML",saveOutput=FALSE)#> ---------------- Alpha=1.5 *** DeltaP=1 *** DeltaM=1 *** LambdaP=1 *** LambdaM=1 *** mu=0 ---------------#> Warning in log(densis): NaNs wurden erzeugt#> *** Iter 1/3 *** Estimated Remaining Time: 0h0min12sec. ***#> *** Iter 2/3 *** Estimated Remaining Time: 0h0min12sec. ***#> Warning in log(densis): NaNs wurden erzeugt#> *** Iter 3/3 *** Estimated Remaining Time: 0h0min0sec. ***colMeans(sweep(res_CTS_ML_size10$outputMat[,9:14],2,thetaT),na.rm=TRUE)#>     alphaE    delta+E    delta-E   lambda+E   lambda-E        muE#> -1.4999990 -0.9999990  9.5255124  7.2885255  0.3178998 -0.7087628