| Summary: | 碩士 === 靜宜大學 === 應用數學研究所 === 93 === Reynolds stress, which can be expressed as a product of two random variables, is one of the main driving forces to initiate the sediment movement for turbulence flow. In order to estimate the Reynolds stress, the method to calculate the tail probability of the product of two random variables was investigated in this paper.
Based on Wood,Booth&Butler(1993) generalization of the typical saddlepoint approximation theorem, a saddlepoint approximation with the double-expontial base was proposed to approximate the tail probability of the product of two random variables. The proposed method was named modified saddlepoint appromimation in this study. Furthermore, this new method was compared with the normal approximation and the typical saddlepoint approximation.
The following four different cases were considered:
a) the product of two independent normal variables
b) the product of two dependent normal variables
c) the product of a normal variable and a contaminated normal variable, which
are independent
d) the product of a normal variable and a contaminated normal variable, which
are dependent
According to the results of this study, the typical and the modified saddlepoint approximations are more accurate than the normal approximation under the cases of (a) and (b). For the cases of (c) and (d), the modified saddlepoint approximation is more accurate than the other two approximations, which was especially true when the kurtosis of the contaminated normal variable was large.
|
|---|
