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Research Article |

Statistical Properties of Points Between Two Random Points

Important inferences in statistics, economics and finance such as mixture distribution fitting in portfolio management are closely related to finding statistical properties of points between two random points. This problem is studied in the literature; however, accurate and fast approximations and Monte Carlo simulations are not well studied. This paper is concerned to finding these properties such as distribution function and moment generating function of points between two random points are derived. To this end, the random linear transformation technique plays important role. Also, the moment generating function is represented as expectation of random variable indexed by a Poisson variable. This note is useful to propose the Monte Carlo simulation of generating function. Two applications in mixture distribution fitting and properties of weighted averages are given. These two applications have been used in the literature for Bayesian bootstrap, change point analysis, DNA segmentations, where all theoretical results may be applied in these fields, directly. Finally, conclusions are presented.

Linear Transformation, Mixture Distribution, Moment Generating Function, Monte Carlo, Random Points

APA Style

Habibi, R. (2024). Statistical Properties of Points Between Two Random Points. Mathematics Letters, 10(1), 7-11.

ACS Style

Habibi, R. Statistical Properties of Points Between Two Random Points. Math. Lett. 2024, 10(1), 7-11. doi: 10.11648/ml.20241001.12

AMA Style

Habibi R. Statistical Properties of Points Between Two Random Points. Math Lett. 2024;10(1):7-11. doi: 10.11648/ml.20241001.12

Copyright © 2024 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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