Theoretical aspects of total time on test transform of weighted variables and applications

Mojtaba Esfahani; Gholam Reza Mohtashami-Borzadaran; Mohammad Amini

Kybernetika (2023)

  • Volume: 59, Issue: 2, page 209-233
  • ISSN: 0023-5954

Abstract

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Although the total time on test (TTT) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the TTT transform for the weighted random variables and investigates the behavior of the failure rate function of such variables based on the TTT transform. In addition, the conditions for establishing the T T T transform ordering for weight variables and its relationship with some stochastic orders have been investigated, and the conditions for establishing the TTT transform order as well as the presentation of the new better than used in total time on test transform (NBUT) class of the weighted variables have also been studied. Finally, by analyzing the real data sets, applications of the transform introduced in the fit of a model is presented, and it is shown that weighted models have a significant advantage over the base models.

How to cite

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Esfahani, Mojtaba, Mohtashami-Borzadaran, Gholam Reza, and Amini, Mohammad. "Theoretical aspects of total time on test transform of weighted variables and applications." Kybernetika 59.2 (2023): 209-233. <http://eudml.org/doc/299077>.

@article{Esfahani2023,
abstract = {Although the total time on test (TTT) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the TTT transform for the weighted random variables and investigates the behavior of the failure rate function of such variables based on the TTT transform. In addition, the conditions for establishing the $TTT$ transform ordering for weight variables and its relationship with some stochastic orders have been investigated, and the conditions for establishing the TTT transform order as well as the presentation of the new better than used in total time on test transform (NBUT) class of the weighted variables have also been studied. Finally, by analyzing the real data sets, applications of the transform introduced in the fit of a model is presented, and it is shown that weighted models have a significant advantage over the base models.},
author = {Esfahani, Mojtaba, Mohtashami-Borzadaran, Gholam Reza, Amini, Mohammad},
journal = {Kybernetika},
keywords = {total time on test transform; generalized failure rate; generalized reversed failure rate; new better than used in total time on test transform; weight function},
language = {eng},
number = {2},
pages = {209-233},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Theoretical aspects of total time on test transform of weighted variables and applications},
url = {http://eudml.org/doc/299077},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Esfahani, Mojtaba
AU - Mohtashami-Borzadaran, Gholam Reza
AU - Amini, Mohammad
TI - Theoretical aspects of total time on test transform of weighted variables and applications
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 2
SP - 209
EP - 233
AB - Although the total time on test (TTT) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the TTT transform for the weighted random variables and investigates the behavior of the failure rate function of such variables based on the TTT transform. In addition, the conditions for establishing the $TTT$ transform ordering for weight variables and its relationship with some stochastic orders have been investigated, and the conditions for establishing the TTT transform order as well as the presentation of the new better than used in total time on test transform (NBUT) class of the weighted variables have also been studied. Finally, by analyzing the real data sets, applications of the transform introduced in the fit of a model is presented, and it is shown that weighted models have a significant advantage over the base models.
LA - eng
KW - total time on test transform; generalized failure rate; generalized reversed failure rate; new better than used in total time on test transform; weight function
UR - http://eudml.org/doc/299077
ER -

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