Modeling real life data through an extension of the power Ailamujia distribution and its AR(1) process
- 1Department of Statistics and Operations Research, College of Science, Qassim University
- 2Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)
- 3Mathematics Department, Faculty of Science, Mansoura University
Abstract
Positive-valued measurements such as failure times, waiting durations, and event intervals frequently arise in reliability engineering, environmental monitoring, and survival analysis. These data often exhibit skewness and non–monotonic hazard behaviour that classical lifetime models, including the exponential and Weibull distributions, fail to capture adequately. This paper proposes a flexible modeling framework for analyzing both independent lifetime observations and dependent positive time-series data. The approach is based on a modified Fréchet transformation applied to a positive baseline distribution, producing a tractable model with a closed-form quantile representation that facilitates simulation and statistical inference. Several statistical properties are derived, and parameter estimation procedures are investigated through Monte Carlo experiments. To account for temporal dependence commonly observed in duration data, a positive-valued first-order autoregressive process is also developed. Applications to real datasets demonstrate improved fitting accuracy and predictive performance compared with commonly used lifetime models. The proposed framework provides a practical and interpretable tool for modeling reliability data, event durations, and asymmetric time-dependent measurements encountered in applied statistical analysis.
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BibTeX
@article{gomaa2026modeling,
title = {{Modeling real life data through an extension of the power Ailamujia distribution and its AR(1) process}},
author = {Rabab S. Gomaa and Mohamed A. Abd Elgawad and Ibtehal Alazman and Fatma M. Mowafy and Beih S. El-Desouky and Shimaa M. El-Hadidy},
journal = {Scientific Reports},
year = {2026},
month = jul,
doi = {10.1038/s41598-026-60751-z},
url = {https://doi.org/10.1038/s41598-026-60751-z},
note = {CC BY},
}
RIS
TY - JOUR
TI - Modeling real life data through an extension of the power Ailamujia distribution and its AR(1) process
AU - Rabab S. Gomaa
AU - Mohamed A. Abd Elgawad
AU - Ibtehal Alazman
AU - Fatma M. Mowafy
AU - Beih S. El-Desouky
AU - Shimaa M. El-Hadidy
PY - 2026
DA - 2026/07/01
JO - Scientific Reports
DO - 10.1038/s41598-026-60751-z
UR - https://doi.org/10.1038/s41598-026-60751-z
AB - Positive-valued measurements such as failure times, waiting durations, and event intervals frequently arise in reliability engineering, environmental monitoring, and survival analysis. These data often exhibit skewness and non–monotonic hazard behaviour that classical lifetime models, including the exponential and Weibull distributions, fail to capture adequately. This paper proposes a flexible modeling framework for analyzing both independent lifetime observations and dependent positive time-series data. The approach is based on a modified Fréchet transformation applied to a positive baseline distribution, producing a tractable model with a closed-form quantile representation that facilitates simulation and statistical inference. Several statistical properties are derived, and parameter estimation procedures are investigated through Monte Carlo experiments. To account for temporal dependence commonly observed in duration data, a positive-valued first-order autoregressive process is also developed. Applications to real datasets demonstrate improved fitting accuracy and predictive performance compared with commonly used lifetime models. The proposed framework provides a practical and interpretable tool for modeling reliability data, event durations, and asymmetric time-dependent measurements encountered in applied statistical analysis.
SN - 2045-2322
ER -