NON-CENTRAL MOMENTS OF THE TRUNCATED NORMAL VARIABLE IN FINANCE

This paper computes the Non-central Moments of the Truncated Normal variable, i.e. a Normal constrained to assume values in the interval with bounds that may be finite or infinite. We define two recursive expressions where one can be expressed in closed form. Another closed form is defined using the Lower Incomplete Gamma Function. Moreover, an upper bound for the absolute value of the Non-central Moments is determined. The numerical results of the expressions are compared and the different behavior for high value of the order of the moments is shown. The limitations to the use of Truncated Normal distributions with a lower negative limit regarding financial products are considered. Limitations in the application of Truncated Normal distributions also arise when considering a CRRA utility function.

Structural reliability and its sensitivity analysis based on the saddlepoint approximation-line sampling method by dichotomy of golden section

In order to solve the structural reliability and its sensitivity of the implicit nonlinear performance function (PF) the advantages of the saddlepoint approximation (SA) and line sampling (LS) are merged. Also, the merits of dichotomy and the solution efficiency of the golden section method are combined to propose the saddlepoint approximation-line sampling (SA-LS) method based on the dichotomy of the golden section point. This is complicated and changeable in the non normal variable space, which is a very hot issue of the present international study. For each sample, it is quick to find its zeropoint in PF along the important line sampling direction by the previously mentioned dichotomy so that the structural failure probability can be transformed into the mean of a series linear PFs failure probability, and the reliability sensitivity is just the derivative or partial one of the probability with respect to the relational variables. Examples show that the SA-LS method based on the dichotomy of the golden section point is of high precision and fast velocity in analyzing the structural reliability and sensitivity of the implicit nonlinear PF that are complicated and changeable in the non-normal variable space.

Fluid Structural Analysis of Human Cerebral Aneurysm Using Their Own Wall Mechanical Properties

Computational Structural Dynamics (CSD) simulations, Computational Fluid Dynamics (CFD) simulation, and Fluid Structure Interaction (FSI) simulations were carried out in an anatomically realistic model of a saccular cerebral aneurysm with the objective of quantifying the effects of type of simulation on principal fluid and solid mechanics results. Eight CSD simulations, one CFD simulation, and four FSI simulations were made. The results allowed the study of the influence of the type of material elements in the solid, the aneurism’s wall thickness, and the type of simulation on the modeling of a human cerebral aneurysm. The simulations use their own wall mechanical properties of the aneurysm. The more complex simulation was the FSI simulation completely coupled with hyperelastic Mooney-Rivlin material, normal internal pressure, and normal variable thickness. The FSI simulation coupled in one direction using hyperelastic Mooney-Rivlin material, normal internal pressure, and normal variable thickness is the one that presents the most similar results with respect to the more complex FSI simulation, requiring one-fourth of the calculation time.

SCALING THRESHOLD CHARACTERS

ABSTRACT A simple method of scaling ordered categorical responses having a joint distribution with an underlying normal variable is presented. Scores are developed that maximize heritability of the observed variate and that in the class of scores based on polychotomies: (1) maximize the correlation between score and the underlying genetic value to be predicted, and (2) minimize mean-square prediction error. Several examples suggest little is lost, in terms of heritability, by using equally spaced scores. The proposed scaling method discriminates among candidates for selection that would be tied if equally spaced scores are used and sometimes yields different rankings of candidates.