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.
| Published in | Mathematics Letters (Volume 10, Issue 1) |
| DOI | 10.11648/ml.20241001.12 |
| Page(s) | 7-11 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Linear Transformation, Mixture Distribution, Moment Generating Function, Monte Carlo, Random Points
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APA Style
Habibi, R. (2024). Statistical Properties of Points Between Two Random Points. Mathematics Letters, 10(1), 7-11. https://doi.org/10.11648/ml.20241001.12
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
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Download@article{10.11648/ml.20241001.12,
author = {Reza Habibi},
title = {Statistical Properties of Points Between Two Random Points},
journal = {Mathematics Letters},
volume = {10},
number = {1},
pages = {7-11},
doi = {10.11648/ml.20241001.12},
url = {https://doi.org/10.11648/ml.20241001.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.ml.20241001.12},
abstract = {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.
},
year = {2024}
}
TY - JOUR T1 - Statistical Properties of Points Between Two Random Points AU - Reza Habibi Y1 - 2024/02/05 PY - 2024 N1 - https://doi.org/10.11648/ml.20241001.12 DO - 10.11648/ml.20241001.12 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 7 EP - 11 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/ml.20241001.12 AB - 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. VL - 10 IS - 1 ER -
Banking Department, Iran Banking Institute, Central Bank of Iran, Tehran, Iran
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