Closed Form Approximation of Swap Exposures

2013 ◽  
Author(s):  
Heikki Sepppll ◽  
Ser-Huang Poon ◽  
Thomas Schrrder
Keyword(s):  
Closed Form ◽  
Closed Form Approximation

Economic Capital Modeling Closed Form Approximation for Real-Time Applications

2014 ◽  
Author(s):  
Thomas Ribarits ◽  
Axel Clement ◽  
Heikki Sepppll ◽  
Hua Bai ◽  
Ser-Huang Poon
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Economic Capital ◽  
Real Time Applications ◽  
Closed Form Approximation

scholarly journals A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

2021 ◽  
Vol 8 (1) ◽  
pp. 33-44
Author(s):  
Toufik Chaayra ◽  
Hussain Ben-azza ◽  
Faissal El Bouanani
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Performance Metrics ◽  
Approximate Expression ◽  
Maximal Ratio Combining ◽  
Generalized Gamma ◽  
The Moment ◽  
Probability Density Function Pdf ◽  
Closed Form Approximation ◽  
Fox’S H Function

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

Dynamical Behaviour of a Materially Damped Flexible Towed Cable

1972 ◽  
Vol 23 (2) ◽  
pp. 109-120 ◽  
Author(s):  
T C Cannon ◽  
J Genin
Keyword(s):  
Closed Form ◽  
Natural Frequencies ◽  
Equilibrium Shape ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Aerodynamic Loading ◽  
Towed Cable ◽  
Closed Form Approximation ◽  
Good Agreement

SummaryThe three-dimensional equations of motion of a flexible towed cable are developed. A closed-form approximation for the equilibrium shape of a cable subjected to arbitrary aerodynamic loading is developed and used in the study of a heavy, vibrating tow cable. Natural frequencies of vibration and cable shapes are computed for typical cables and are shown to be in good agreement with exact, numerically obtained values.

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