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Pakgohar, Alireza, Shokri, Soheil. (1405). Topp-Leone Distribution: A Reliability Analysis Perspective. فصلنامه علمی زیست فناوری گیاهان زراعی, (), -. doi: 10.30473/jaslda.2026.77349.1001
Alireza Pakgohar; Soheil Shokri. "Topp-Leone Distribution: A Reliability Analysis Perspective". فصلنامه علمی زیست فناوری گیاهان زراعی, , , 1405, -. doi: 10.30473/jaslda.2026.77349.1001
Pakgohar, Alireza, Shokri, Soheil. (1405). 'Topp-Leone Distribution: A Reliability Analysis Perspective', فصلنامه علمی زیست فناوری گیاهان زراعی, (), pp. -. doi: 10.30473/jaslda.2026.77349.1001
Pakgohar, Alireza, Shokri, Soheil. Topp-Leone Distribution: A Reliability Analysis Perspective. فصلنامه علمی زیست فناوری گیاهان زراعی, 1405; (): -. doi: 10.30473/jaslda.2026.77349.1001

Topp-Leone Distribution: A Reliability Analysis Perspective

Journal of Advances in Statistical Learning and Data Analysis
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 مهر 1405    اصل مقاله (2.01 M)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.30473/jaslda.2026.77349.1001
نویسندگان
Alireza Pakgohar* 1؛ Soheil Shokri2
1Department of Statistics, Payame Noor University, Tehran, Iran
2Department of Mathematics and Statistics, Ra.C., Islamic Azad University, Rasht, Iran.
چکیده
This article presents a comprehensive investigation into
the structural and reliability properties of the Topp-Leone distribution.
A primary contribution of this study is the derivation of an exact
finite series representation for the probability density function of order
statistics, which rectifies previous approximation-based approaches.
Furthermore, closed-form expressions for key information-theoretic
measures, including Shannon entropy, extropy, and divergence metrics
(e.g., Kullback-Leibler and R´enyi), are established to quantify uncertainty
and distributional disparity. The applicability of the TL distribution in
system reliability is also examined through the stress-strength model.
Collectively, these analytical results elucidate the theoretical foundations
of the TL distribution and underscore its potential in statistical inference
and reliability engineering contexts. 

تازه های تحقیق

  • Derives an exact finite-series representation for the density of Topp–Leone order statistics.

  • Establishes closed-form expressions for Shannon entropy and extropy.

  • Investigates Kullback–Leibler and Rényi divergence measures.

  • Examines stress–strength reliability under the Topp–Leone distribution.

  • Provides analytical insights for statistical inference and reliability engineering.

 
کلیدواژه‌ها
Divergence measures؛ Order statistics؛ Stress-strength؛ Information theory
مراجع

[1] Almetwally, E. M. (2021). The odd Weibull inverse Topp–Leone distribution with applications
to COVID-19 data. Annals of Data Science, 9 (1), 121–140. https://doi.org/10.1007/
s40745-021-00329-w 
[2] Alghamdi, S. M., Albalawi, O., Almarzouki, S. M., Nagarjuna, V. B. V., Nasiru, S., &
Elgarhy, M. (2024). Different estimation methods of the modified Kies T-L model with
applications and quantile regression. PLoS ONE, 19 (9), e0307391. https://doi.org/10.
1371/journal.pone.0307391 
[3] Buono, F., & Longobardi, M. (2020). A dual measure of uncertainty: The Deng extropy.
Entropy, 22 (5), 582. https://doi.org/10.3390/e22050582 

[4] Galton, F. (1883). Inquiries into human faculty and its development. Macmillan. https:
//digitalcommons.rockefeller.edu/jason-brown-library/84 
[5] Gen¸c, A. I. (2012). Moments of order statistics of Topp-Leone distribution. Statistical Papers,
53 (1), 117–131.https://doi.org/10.1007/s00362-010-0320-y pages 3
[6] Gen¸c, A. I. (2013). Estimation of P(X ¿ Y) with Topp–Leone distribution. Journal of Statistical Computation and Simulation, 83 (2), 326–339. https://doi.org/10.1080/00949655.
2011.607821 
[7] Giles, D. (2012). A note on improved estimation for the Topp-Leone distribution (Econometrics Working Paper EWP1203). https://web.uvic.ca/~dgiles/downloads/working_
papers/ewp1203.pdf 
[8] Ghitany, M. E., Kotz, S., & Xie, M. (2005). On some reliability measures and their stochastic
orderings for the Topp-Leone distribution. Journal of Applied Statistics, 32 (7), 715–722.
https://doi.org/10.1080/02664760500079613 pages 2, 3, 11
[9] Kotz, S., & Seier, E. (2007). Kurtosis of the Topp-Leone distributions. Interstat, 1, 1–15.

[10] Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22 (1), 79–86. http://dx.doi.org/10.1214/aoms/1177729694 
[11] Lad, F., Sanfilippo, G., & Agr`o, G. (2015). Extropy: Complementary dual of entropy.
Statistical Science, 30 (1). https://doi.org/10.1214/14-sts430 
[12] Metwally, A. S. M., Hassan, A. S., Almetwally, E. M., Kibria, B. M. G., & Almongy, H. M.
(2021). Reliability analysis of the new exponential inverted Topp–Leone distribution with
applications. Entropy, 23 (1), Article 28. https://doi.org/10.3390/e23010028
[13] MirMostafaee, S. M. T. K. (2014). On the moments of order statistics coming from the
Topp–Leone distribution. Statistics & Probability Letters, 95, 85–91. https://doi.org/10.
1016/j.spl.2014.08.014 
[14] Moors, J. J. A. (1988). A quantile alternative for kurtosis. The Statistician, 37 (1), 25–32.
https://doi.org/10.2307/2348376 
[15] Nadarajah, S., & Kebe, M. (2023). Explicit expressions for most common entropies. Entropy,
25 (3), 534. https://doi.org/10.3390/e25030534 
[16] Pakgohar, A. (2024). Exploring the Burr type III distribution: Properties, stochastic orders,
and information measures. Journal of Statistical Modeling: Theory and Applications, 5 (1),
165–180. https://doi.org/10.22034/jsmta.2025.21694.1143 
[17] Pakgohar, A., & Yousefzadeh, F. (2025). A quantile approach to the Kullback-Leibler
divergence on type-I censored variable and record values. Journal of Mathematical Extension,
19 (1), 1–18. https://doi.org/10.30495/JME.2025.3093
[18] Pakgohar, A., Habibirad, A., & Yousefzadeh, F. (2019). Lin–Wong divergence and relations
on type I censored data. Communications in Statistics—Theory and Methods, 48 (19),
4804–4819. https://doi.org/10.1080/03610926.2018.1494839 

[19] Pourdarvish, A., MirMostafaee, S. M. T. K., Fayyaz Movaghar, A., & Naderi, K. (2015).
On the estimation of the shape parameter of the Topp-Leone distribution. Annual Iranian
Mathematics Conference. SID. https://sid.ir/paper/920884/en 
[20] Qian, H., Wang, B. X., Zhou, H., & Wang, S. (2025). Interval estimation for Topp-Leone
distribution. Communications in Statistics—Theory and Methods, 1–22. https://doi.org/
10.1080/03610926.2024.2447847 
[21] Rezaei, S., Sadr, B. B., Alizadeh, M., & Nadarajah, S. (2017). Topp-Leone generated family
of distributions: Properties and applications. Communications in Statistics—Theory and
Methods, 46 (3), 1177–1197. https://doi.org/10.1080/03610926.2015.1053935 
[22] Sangsanit, Y., & Bodhisuwan, W. (2016). The Topp-Leone generator of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics,
45 (6), 1835–1848.https://web.archive.org/web/20180422022254id_/http://rdo.psu.
ac.th/sjstweb/journal/38-5/38-5-9.pdf 
[23] Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE
Mobile Computing and Communications Review, 5 (1), 3–55. https://doi.org/10.1145/
584091.584093
[24] Topp, C. W., & Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the
American Statistical Association, 50 (269), 209–219. https://doi.org/10.1080/01621459.
1955.10501259

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