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Peer-reviewedCC BY 4.0Mathematics

A New Topp–Leone Juchez Distribution with Applications to Accelerated Life-Test and Aircraft Window-Glass Strength Data

  • Ayşe Metin Karakaş1
  • Fatma Bulut2
  • Murat Karakaş2
  • Sinan Çalık3
  1. 1Department of Statistics, Faculty of Arts and Sciences, Bitlis Eren University, Bitlis 13000, Türkiye
  2. 2Department of Mathematics, Faculty of Arts and Sciences, Bitlis Eren University, Bitlis 13000, Türkiye
  3. 3Department of Statistics, Faculty of Science, Firat University, Elazig 23119, Türkiye
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Abstract

This study introduces the Topp–Leone Juchez (TLJ) distribution, a flexible two-parameter lifetime model constructed from the one-parameter Juchez distribution through the Topp–Leone transformation. The proposed model provides additional shape and hazard-rate flexibility while remaining parsimonious. Several distributional and reliability properties are derived, including the survival and hazard functions, quantile function, moments, entropy measures, and stress–strength reliability. Classical and Bayesian estimation procedures are investigated, and their finite-sample performance is examined through Monte Carlo simulations. Two real-data applications involving accelerated life-test and aircraft window-glass strength data are also considered. The results show that the TLJ model provides competitive fits relative to several established lifetime distributions. For the aircraft window-glass data, the TLJ and Gamma models provide very similar empirical support, with an AIC difference of only 0.0858. Importantly, the TLJ model is not a nested extension of the Juchez distribution, since setting α=1 does not recover the original Juchez model. Overall, the results demonstrate the usefulness of the TLJ construction as a flexible alternative for lifetime-data analysis.

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Cite

BibTeXRIS
BibTeX
@article{karakas2026toppleone,
  title = {{A New Topp–Leone Juchez Distribution with Applications to Accelerated Life-Test and Aircraft Window-Glass Strength Data}},
  author = {Ayşe Metin Karakaş and Fatma Bulut and Murat Karakaş and Sinan Çalık},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203804},
  url = {https://www.mdpi.com/2227-7390/14/20/3804},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A New Topp–Leone Juchez Distribution with Applications to Accelerated Life-Test and Aircraft Window-Glass Strength Data
AU  - Ayşe Metin Karakaş
AU  - Fatma Bulut
AU  - Murat Karakaş
AU  - Sinan Çalık
PY  - 2026
DA  - 2026/10/20
JO  - Mathematics
DO  - 10.3390/math14203804
UR  - https://www.mdpi.com/2227-7390/14/20/3804
AB  - This study introduces the Topp–Leone Juchez (TLJ) distribution, a flexible two-parameter lifetime model constructed from the one-parameter Juchez distribution through the Topp–Leone transformation. The proposed model provides additional shape and hazard-rate flexibility while remaining parsimonious. Several distributional and reliability properties are derived, including the survival and hazard functions, quantile function, moments, entropy measures, and stress–strength reliability. Classical and Bayesian estimation procedures are investigated, and their finite-sample performance is examined through Monte Carlo simulations. Two real-data applications involving accelerated life-test and aircraft window-glass strength data are also considered. The results show that the TLJ model provides competitive fits relative to several established lifetime distributions. For the aircraft window-glass data, the TLJ and Gamma models provide very similar empirical support, with an AIC difference of only 0.0858. Importantly, the TLJ model is not a nested extension of the Juchez distribution, since setting α=1 does not recover the original Juchez model. Overall, the results demonstrate the usefulness of the TLJ construction as a flexible alternative for lifetime-data analysis.
SN  - 2227-7390
ER  -