Based on the compound Poisson risk process that is perturbed by
    a Brownian motion, saddlepoint approximations to some measures of risk are
    provided. Various approximation methods for the probability of ruin are
    also included. Furthermore, exact values of both the risk measures as well
    as the probability of ruin are available if the individual claims follow
    a hypo-exponential distribution (i. e., if it can be represented as a sum
    of independent exponentially distributed random variables with different
    rate parameters). For more details see Gatto and Baumgartner (2014)
    <doi:10.1007/s11009-012-9316-5>.

We visualize the standard deviation of a data set as the size of a prism whose volume equals the total volume of several prisms made from the Empirical Cumulative Distribution Function.

Solves the general Semi-Definite Linear Programming formulation using an R implementation of SDPT3 (K.C. Toh, M.J. Todd, and R.H. Tutuncu (1999) <doi:10.1080/10556789908805762>). This includes problems such as the nearest correlation matrix problem (Higham (2002) <doi:10.1093/imanum/22.3.329>), D-optimal experimental design (Smith (1918) <doi:10.2307/2331929>), Distance Weighted Discrimination (Marron and Todd (2012) <doi:10.1198/016214507000001120>), as well as graph theory problems including the maximum cut problem. Technical details surrounding SDPT3 can be found in R.H Tutuncu, K.C. Toh, and M.J. Todd (2003) <doi:10.1007/s10107-002-0347-5>.

The sdrt() function is designed for estimating subspaces for Sufficient Dimension Reduction (SDR) in time series, with a specific focus on the Time Series Central Mean subspace (TS-CMS). The package employs the Fourier transformation method proposed by Samadi and De Alwis (2023) <doi:10.48550/arXiv.2312.02110> and the Nadaraya-Watson kernel smoother method proposed by Park et al. (2009) <doi:10.1198/jcgs.2009.08076> for estimating the TS-CMS. The package provides tools for estimating distances between subspaces and includes functions for selecting model parameters using the Fourier transformation method.