.svg){kind=logo}
A NEW TRUNCATED PROBABILITY DISTRIBUTION: MODEL, PROPERTIES, ROBUSTNESS STUDY AND APPLICATION
Keywords:
Hypoexponential distribution, Estimation, Log concavity, Right truncation, Robustness study, Real data analysis.DOI:
https://doi.org/10.17654/0972361724039Abstract
Truncated distributions play a significant role in analyzing problems of epidemiology, material science, production process, process optimization, psychology, social sciences, statistics and quality improvement, where one wants to study about data which lie above or below a given threshold or within a specified range. A reason for truncation is that there is no interest beyond the truncation point. Right truncation happens when the occurrence is limited to values which lie above the truncation point. In this article, we develop and analyze a right truncated version of hypoexponential distribution beyond the interval $(0, b)$. Various distributional and reliability properties of the proposed distribution are investigated. Using vinyl chloride data, a real data analysis is carried out.
Received: December 29, 2023
Revised: April 2, 2024
Accepted: April 11, 2024
References
S. Abid and R. Abdulrazak, truncated Frechet-Weibull and Frechet distributions, International Journal of Research in Industrial Engineering 7(1) (2018), 106-135.
M. P. Adams, Integral, mean and covariance of the simplex-truncated multivariate normal distribution, PLoS ONE 17(7) (2022), 1-31.
M. M. Ali and S. Nadarajah, Truncated Pareto distribution, Computer Communications 30(1) (2006), 1-4.
N. Alotaibi, I. Elbatal, E. M. Almetwally, S. A. Alyami, A. S. Al-Moisheer and M. Elgarhy, Truncated Cauchy power Weibull-G class of distributions: Bayesian and non-Bayesian inference modelling for COVID-19 and carbon fiber data, Mathematics 10(9) (2022), 1-25.
S. H. Amal, A. H. S. Mohamed and M. E. Ahmed, A new family of upper-truncated distributions: properties and estimation, Thail. Stat. 18(2) (2020), 196-214.
B. Anjum and H. G. Perros, Adding percentiles of Erlangian distributions, IEEE Commun. Lett. 15(3) (2011), 346-348.
K. Anithakumari, K. Srinivas Rao and P. R. S. Reddy, On a right truncated generalized Gaussian distribution, Research Journal of Mathematical and Statistical Sciences 3(4) (2015(a)), 1-9.
K. Anithakumari, K. Srinivas Rao and P. R. S. Reddy, On a left truncated generalized Gaussian distribution, Journal of Advance Computing 4(1) (2015(b)), 1-21.
E. Altun, Weighted exponential regression model: an alternative to the gamma regression model, Int. J. Model. Simul. Sci. Comput. 10 (2019), 1-15.
E. Altun, The Lomax regression model with residual analysis, J. Appl. Stat. 10 (2020), 1-10.
M. Z. Arshad, O. S. Balogum, M. Z. Iqbal and P. E. Oguntunde, Exponentiated left truncated power distribution: On some properties of a new truncated model with applications to life time data, International Journal of Analysis and Applications 20 (2022), 20-23.
T. F. Bateson, Gamma regression of interevent waiting times versus poisson regression of daily event counts: inside the epidemiologists tool-box selecting the best modeling tools for the job, Epidemiology 20 (2009), 202-204.
G. Bolch, S. Grenier, H. D. Meer and K. S. Trivedi, Chapter 1, Introduction, Queuing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, 2nd ed., Wiley-Blackwell, 2006.
E. Cepada and D. Gamerman, Bayesian methodology for modeling parameters in the two parameter exponential family, Revista Estadistica 57 (2005), 93-105.
D. Chapman, Estimating the parameters of a truncated Gamma distribution, Annals of Mathematical Statistics 27(2) (1956), 498-506.
P. Consentino, V. Fiearra and D. Luzio, Truncated exponential frequency magnitude relationship in earthquake statistics, Bull. Seismol. Soc. Amer. 67(6) (1977), 1615-1623.
E. C. Cuervo, Modelagem da variabilidade emmodeloslinears generalizados, Doctoral dissertation, Tese de D.Sc., IM-UFRJ, Rio de Janeiro, RJ, Brasil, 2001.
H. H. El-Damrawy, A. A. M. Teamah and B. M. El-Shiekh, Truncated bivariate Kumaraswamy exponential distribution, Journal of Statistics Applications and Probability 11(2) (2022), 461-469.
F. Galton, An examination in the registered speeds of American trotting horses, with remarks on their value as hereditary data, Proceedings of the Royal Society of London 62(1) (1898), 310-315.
A. Gul, M. Mohsin, M. Adil and M. Ali, A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data, PLoS ONE 16(4) (2021), 1-24.
H. A. A. Hashim and K. A. Al-Kadim, Right truncated of mixture Topp-Leone with exponential distribution, Journal of Physics: Conference Series 1804(1) (2021), 1-9.
H. M. Hussein and M. T. Ahmed, Family of truncated Gompertz-exponential distribution with properties and application, Turkish Journal of Computer and Mathematics 12(14) (2021), 1383-1399.
G. Indranil and B. Marcelo, A new extended Burr XII distribution, Austrian Journal of Statistics 46(1) (2017), 33-39.
T. Kadri, K. Smaili and S. Kadry, Markov modeling for reliability analysis using hypoexponential distribution, Numerical Methods for Reliability and Safety Assessment, Springer, 2015, pp. 599-620.
T. Kadri, K. Smaili, S. Kadry and A. Joubbch, On the product of two hypoexponential random variables, BAU Journal-Science and Technology 1(1) (2019), 1-10.
S. Kotz and S. Nadarajah, Multivariate t Distributions and their Applications, Cambridge University Press, New York, 2004.
S. Nadarajah and S. Kotz, A truncated Cauchy distribution, International Journal of Mathematical Education in Science and Technology 37(5) (2006), 605-608.
A. S. Nik, C. Chesneau, H. S. Bakouch and A. Asgharzadeh, A new truncated -F family of lifetime distributions with an extensive study to a sub model and reliability data, Africa Mathematica 34(3) (2023), 1-17.
A. Orabi, B. Ahmed and D. Ziedan, A new class of the Weibull-generalized truncated Poisson distribution for reliability and life data analysis, Appl. Math. Sci. 16(3) (2022), 139-150.
K. Pearson and A. Lee, On the generalized probable error in multiple normal correlation, Biometrika 6(1) (1908), 59-68.
L. D. Ribeiro-Reis, Truncated exponentiated exponential distribution: a class for unit interval, Journal of Statistics and Management Systems 25 (2022), 2061 2072.
G. E. Willmot and J. K. Woo, On the class of Erlang mixtures with risk theoretic applications, North American Actuarial Journal 11(2) (2007), 99-115.
L. Zaninetti, The initial mass function modeled by a left truncated beta distribution, The Astrophysical Journal 765(2) (2013), 128-135.
T. Zhang and M. Xie, On the upper truncated Weibull distribution and its reliability implications, Reliability Engineering and System Safety 96(1) (2011), 194-200.
Downloads
Published
Versions
- 25-04-2025 (2)
- 25-04-2024 (1)
Issue
Section
License
Copyright (c) 2024 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
