The Lambert-Topp-Leone distribution: an alternative for modeling proportion and lifetime data

被引：0

作者：

Astorga, Juan M. ^{[1
]}

Iriarte, Yuri A. ^{[2
]}

机构：

[1] Univ Atacama, Fac Tecnol, Dept Tecnol Energia, Copiapo, Chile

[2] Univ Antofagasta, Fac Ciencias Bas, Dept Estadist & Ciencia Datos, Antofagasta, Chile

来源：

FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS | 2025年 / 11卷

关键词：

goodness-of-fit; kurtosis; Lambert generator; lifetime data; maximum likelihood estimation; proportion data; skewness; FAMILY; RELIABILITY; MOMENTS;

D O I：

10.3389/fams.2025.1527833

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article discusses the Lambert-Topp-Leone distribution as a flexible alternative for modeling proportion and lifetime data. By extending the Topp-Leone distribution, the proposed model offers greater flexibility in terms of skewness and kurtosis, making it suitable for a broader range of real-world applications. We examine key properties of the distribution, including its moments and behavior in terms of skewness and kurtosis. Parameter estimation using the maximum likelihood method is also discussed. A Monte Carlo simulation study is conducted to evaluate the performance of the estimators. Finally, to illustrate its practical utility, we apply the Lambert-Topp-Leone distribution to real-world datasets, demonstrating its superior fit for proportion and lifetime data compared to traditional models. The results suggest that this distribution provides a valuable tool for researchers and professionals in fields that require versatile modeling of bounded or positively skewed data.

引用

页数：12

共 35 条

[1] Topp C.W., Leone F.C., A family of J-shaped frequency functions, J Am Stat Assoc, 50, pp. 209-219, (1955)
[2] Nadarajah S., Kotz S., Moments of some J-shaped distributions, J Appl Stat, 30, pp. 311-317, (2003)
[3] Ghitany M., Kotz S., Xie M., On some reliability measures and their stochastic orderings for the Topp-Leone distribution, J Appl Stat, 32, pp. 715-722, (2005)
[4] Zhou M., Yang D., Wang Y., Nadarajah S., Some J-shaped distributions: sums, products and ratios, RAMS'06. Annual Reliability and Maintainability Symposium, 2006, (2006)
[5] Kotz S., Seier E., Kurtosis of the Topp-Leone distributions, Interstat, 1, pp. 1-15, (2007)
[6] Nadarajah S., Bathtub-shaped failure rate functions, Qual Quant, 43, pp. 855-863, (2009)
[7] Genc A.I., Moments of order statistics of Topp-Leone distribution, Stat Pap, 53, pp. 117-131, (2012)
[8] Marshall A.W., Olkin I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84, pp. 641-652, (1997)
[9] Eugene N., Lee C., Famoye F., Beta-normal distribution and its applications, Commun Stat-Theory Methods, 31, pp. 497-512, (2002)
[10] Zografos K., Balakrishnan N., On families of beta-and generalized gamma-generated distributions and associated inference, Stat Methodol, 6, pp. 344-362, (2009)

← 1 2 3 4 →