Journals / Gazi University Journal of Science / 2022 / Cilt: 35 - Sayı: 4

Estimating the Parametric Functions and Reliability Measures for Exponentiated Lifetime Distributions Family

Pages
1665–1684
Publication Date
2022-12-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, some real data has been taken to conduct an analysis and to discuss the effectiveness and advantages of the established work by comparing with other methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The paper aims are to extend the theory to estimate the parameters of the exponentiated lifetime distribution.
📊
Key Findings & Data:For it, in this paper, we derived the probability density function, cumulative density, reliability function and the stress-strength parameter of the distribution.
💡
Conclusion & Impact:Finally, some real data has been taken to conduct an analysis and to discuss the effectiveness and advantages of the established work by comparing with other methods.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Exponentiated distributions family · Reliability function · Stress-strength parameter

Abstract

The paper aims are to extend the theory to estimate the parameters of the exponentiated lifetime distribution. For it, in this paper, we derived the probability density function, cumulative density, reliability function and the stress-strength parameter of the distribution. To estimate the parameters of such distribution, we considered the maximum likelihood and uniformly minimum variance unbiased methods. The validity of the proposed work has been conducted over the simulation study of both estimation methods under the special sub model as exponentiated inverse Gompertz distribution. Finally, some real data has been taken to conduct an analysis and to discuss the effectiveness and advantages of the established work by comparing with other methods.

🔖

Cite This Article

POURREZA, H., JAMKHANEH, E. B., DEİRİ, E., GARG, H. (2022). Estimating the Parametric Functions and Reliability Measures for Exponentiated Lifetime Distributions Family. Gazi University Journal of Science, Cilt: 35 - Sayı: 4, 1665–1684. https://ajindex.com/articles/859462

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. Mudholkar, G. S., Srivastava, D. K.,“Exponentiated Weibull family for analyzing bathtub failure-real data”, IEEE Transaction Reliability, 42:299-302, (1993).
  2. Mudholkar, G. S., Srivastava, D. K., Freimes, M.,“The exponentiated Weibull family: A reanalysis of the bus-motor-failure data”, Technometrics, 37: 436-445, (1995).
  3. Nadarajah, S., Kotz, S.,“The Exponentiated Type Distributions”, Acta Applicandae Mathematicae, 92: 97-111, (2006).
  4. Delgarm, L., Zadkarami, M. R.,“A new generalization of lifetime distributions”, Computational Statistics, 30: 1185-1198, (2015).
  5. Pourreza, H., Baloui Jamkhaneh, E., Deiri, E.,“A family of Gamma-generated distributions: Statistical properties and applications”, Statistical Methods in Medical Research, 30(8): 1850-1873, (2021).
  6. Dixit, U. J., Jabbari Nooghabi, M.,“Efficient estimation in the Pareto distribution”, Statistical Methodology, 7(6): 687-691, (2010).
  7. Bagheri, S. F., Alizadeh, M., Nadarajah, S., Deiri, E.,“Efficient estimation of the PDF and the CDF of the Weibull extension model”, Communications in Statistics-Simulation and Computation, 45(6): 2191-2207, (2014).
  8. Bagheri, S. F., Alizadeh, M., Nadarajah, S.,“Efficient estimation of the PDF and the CDF of the exponentiated Gumbel distribution”, Communications in Statistics-Simulation and Computation, 45(1): 339-361, (2016).
  9. Alizadeh, M., Bagheri, S. F., Baloui Jamkhaneh, E., Nadarajah, S.,“Estimates of the PDF and the CDF of the exponentiated Weibull distribution”, Brazilian Journal of Probability and Statistics, 29(3): 695-716, (2015).
  10. Alizadeh, M., Razaei, S., Bagheri, S. F., Nadarajah, S.,“Efficient estimation for the generalized exponential distribution”, Statistical Papers, 56(4): 1015-1031, (2015).
  11. Maiti, S. S., Mukherjee, I.,“On estimation of the PDF and CDF of the Lindley distribution”, Communications in Statistics - Simulation and Computation, 47(5): 1370-1381, (2018).
  12. Ghasemi Cherati, M., Baloui Jamkhaneh, E., Deiri, E.,“Some estimation procedures of the PDF and CDF of the generalized inverted Weibull distribution with comparison”, International Journal of Nonlinear Analysis and Applications, 12(1): 1017-1036, (2021).
  13. Bekker, A., Roux, J.,“Reliability characteristics of the Maxwell distribution: a Bayes estimation study”, Communication in Statistics-Theory and Methods, 34: 2169-2178, (2005).
  14. Krishna, H., Kumar, K.,“Reliability estimation in Lindley distribution with progressively type II right censored sample”, Mathematics and Computer in Simulation, 82: 281-294