Lizhi Niu , Mario Di Paola , Antonina Pirrotta , Wei Xu
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引用次数: 0
摘要
本文首次介绍了一种利用拉普拉斯变换重建随机变量概率密度函数(PDF)的单边 PDF 方法。这种方法定义了新的复杂量,称为移位特征函数,可以使用经典的傅里叶级数展开计算 PDF。然后,通过重新定义双面拉普拉斯变换,将该方法扩展到处理双面 PDF。即使反拉普拉斯变换中的积分沿虚轴离散,这一新定义仍然适用。为了便于比较,还引入了基于梅林变换的双面复分数矩的新定义,以解决 PDF 重构过程中出现的零点奇异性问题。
Laplace and Mellin transform for reconstructing the probability distribution by a limited amount of information
A method for reconstructing the Probability Density Function (PDF) of a random variable using the Laplace transform is first introduced for one-sided PDFs. This approach defines new complex quantities, referred as Shifted Characteristic Functions, which allow the PDF to be computed using a classical Fourier series expansion. The method is then extended to handle double-sided PDFs by redefining the double-sided Laplace transform. This new definition remains applicable even when the integral in the inverse Laplace transform is discretized along the imaginary axis. For comparison, a new definition of double-sided Complex Fractional Moments based on Mellin transform is also introduced, addressing the singularity at zero that arises during PDF reconstruction.
期刊介绍:
This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.