dKRTS

The probability density function (PDF) of the Kim-Rachev tempered stable
distributions is not available in closed form.
Relies on fast Fourier transform (FFT) applied to the characteristic
function.

A collection of methods to estimate parameters of different tempered stable
distributions (TSD). Currently, there are seven different tempered stable
distributions to choose from: Tempered stable subordinator distribution,
classical TSD, generalized classical TSD, normal TSD, modified TSD, rapid
decreasing TSD, and Kim-Rachev TSD.
The package also provides functions to compute density and probability
functions and tools to run Monte Carlo simulations.
This package has already been used for the estimation of tempered stable
distributions (Massing (2023) <arXiv:2303.07060>).
The following references form the theoretical background for various functions
in this package. References for each function are explicitly listed in its
documentation:
Bianchi et al. (2010) <doi:10.1007/978-88-470-1481-7_4>
Bianchi et al. (2011) <doi:10.1137/S0040585X97984632>
Carrasco (2017) <doi:10.1017/S0266466616000025>
Feuerverger (1981) <doi:10.1111/j.2517-6161.1981.tb01143.x>
Hansen et al. (1996) <doi:10.1080/07350015.1996.10524656>
Hansen (1982) <doi:10.2307/1912775>
Hofert (2011) <doi:10.1145/2043635.2043638>
Kawai & Masuda (2011) <doi:10.1016/j.cam.2010.12.014>
Kim et al. (2008) <doi:10.1016/j.jbankfin.2007.11.004>
Kim et al. (2009) <doi:10.1007/978-3-7908-2050-8_5>
Kim et al. (2010) <doi:10.1016/j.jbankfin.2010.01.015>
Kuechler & Tappe (2013) <doi:10.1016/j.spa.2013.06.012>
Rachev et al. (2011) <doi:10.1002/9781118268070>.

Till Massing

TempStable

A Collection of Methods to Estimate Parameters of Different
Tempered Stable Distributions

Cedric Maximilian Juessen

dKRTS function

<dl><dt>x</dt>
<dd>A numeric vector of positive quantiles.</dd>
<dt>alpha</dt>
<dd>Stability parameter. A real number between 0 and 1.</dd>
<dt>kp, km, rp, rm</dt>
<dd>Parameter of KR-distribution. A real number <code>&gt;0</code>.</dd>
<dt>pp, pm</dt>
<dd>Parameter of KR-distribution. A real number <code>&gt;-alpha</code>.</dd>
<dt>mu</dt>
<dd>A location parameter, any real number.</dd>
<dt>theta</dt>
<dd>Parameters stacked as a vector.</dd>
<dt>dens_method</dt>
<dd>Algorithm for numerical evaluation. Here you can only
choose <code>"FFT"</code>.</dd>
<dt>a</dt>
<dd>Starting point of FFT, if <code>dens_method == "FFT"</code>. -20
by default.</dd>
<dt>b</dt>
<dd>Ending point of FFT, if <code>dens_method == "FFT"</code>. 20
by default.</dd>
<dt>nf</dt>
<dd>Pieces the transformation is divided in. Limited to power-of-two
size. 256 by default.</dd></dl>

Arguments

Density Function of the Kim-Rachev tempered stable distribution — dKRTS

<dl>

<dt>x</dt>
<dd>A numeric vector of positive quantiles.</dd>


<dt>alpha</dt>
<dd>Stability parameter. A real number between 0 and 1.</dd>


<dt>kp, km, rp, rm</dt>
<dd>Parameter of KR-distribution. A real number <code>&gt;0</code>.</dd>


<dt>pp, pm</dt>
<dd>Parameter of KR-distribution. A real number <code>&gt;-alpha</code>.</dd>


<dt>mu</dt>
<dd>A location parameter, any real number.</dd>


<dt>theta</dt>
<dd>Parameters stacked as a vector.</dd>


<dt>dens_method</dt>
<dd>Algorithm for numerical evaluation. Here you can only
choose <code>"FFT"</code>.</dd>


<dt>a</dt>
<dd>Starting point of FFT, if <code>dens_method == "FFT"</code>. -20
by default.</dd>


<dt>b</dt>
<dd>Ending point of FFT, if <code>dens_method == "FFT"</code>. 20
by default.</dd>


<dt>nf</dt>
<dd>Pieces the transformation is divided in. Limited to power-of-two
size. 256 by default.</dd>

</dl>

dKRTS: Density Function of the Kim-Rachev tempered stable distribution

Description

Usage

Value

Arguments

Details