pMTS

The cumulative probability distribution function (CDF) of the modified
tempered stable distribution.

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

pMTS function

<dl><dt>q</dt>
<dd>A vector of real numbers where the CF is evaluated.</dd>
<dt>alpha</dt>
<dd>Stability parameter. A real number between 0 and 2.</dd>
<dt>delta</dt>
<dd>Scale parameter. A real number &gt; 0.</dd>
<dt>lambdap, lambdam</dt>
<dd>Tempering parameter. A real number &gt; 0.</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>A method to get the density function. Here, only "FFT" is
available.</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.</dd>
<dt>...</dt>
<dd>Possibility to modify <code><a href="/link/stats%3A%3Aintegrate()?package=TempStable&version=0.2.2" data-mini-rdoc="TempStable::stats::integrate()">stats::integrate()</a></code>.</dd></dl>

Arguments

Cumulative probability function of the  modified tempered stable (MTS)
distribution — pMTS

<dl>

<dt>q</dt>
<dd>A vector of real numbers where the CF is evaluated.</dd>


<dt>alpha</dt>
<dd>Stability parameter. A real number between 0 and 2.</dd>


<dt>delta</dt>
<dd>Scale parameter. A real number &gt; 0.</dd>


<dt>lambdap, lambdam</dt>
<dd>Tempering parameter. A real number &gt; 0.</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>A method to get the density function. Here, only "FFT" is
available.</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.</dd>


<dt>...</dt>
<dd>Possibility to modify <code><a href='https://rdrr.io/r/stats/integrate.html'>stats::integrate()</a></code>.</dd>

</dl>

pMTS: Cumulative probability function of the modified tempered stable (MTS) distribution

Description

Usage

Value

Arguments

Details