Galoitica: Journal of Mathematical Structures and Applications

Journal DOI

https://doi.org/10.54216/GJSMA

Submit Your Paper

2834-5568ISSN (Online)

Volume 11 , Issue 2 , PP: 01-14, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data

Shams Najy Elaiwey 1 * , Mahdi Wahab Neama 2

  • 1 Department of statistics, Faculty of Administration & Economics, University of Kerbala, Kerbala, Iraq - (shams.n@s.uokerbala.edu.iq)
  • 2 Department of statistics, Faculty of Administration & Economics, University of Kerbala, Kerbala, Iraq - (mehdi.wahab@uokerbala.edu.iq)
  • Doi: https://doi.org/10.54216/GJMSA.0110201

    Received: December 02, 2023 Revised: March 28, 2024 Accepted: July 24, 2024
    Abstract

    In this paper, we propose a novel generalization for one parameter inverse Lindley distribution to fitting monotonically descending data named the T-ILD{Y} distribution class ,   T is one parameter inverse exponential distribution ,  R has an one parameter inverse Lindley distribution , and the variable Y is one parameter exponential distribution, the resulting distribution is inverse exponential- inverse Lindley- exponential (IEILDE). The theory of fuzzy sets  are used by converting the distribution to fuzzy by using  a fuzzy triangular distribution based on the quantile function (FIEILE), the maximum likelihood , and the maximum likelihood, and  the maximum product spacing method were used estimate the parameters of the distribution. We conclude that at cutoff α=0.1, ML is better than the MPS, and at cutoff coefficients α=0.3, 0.5, 0.7, MPS was better than the ML, The higher the cutoff, the better the maximum likelihood method.

    Keywords :

    fuzzy distribution , Quantile Function , monotonically , Lindley distribution Maximum Likelihood , Maximum Product spacing

    References

    [1]       Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. METRON 2013;71:63–79. https://doi.org/10.1007/s40300-013-0007-y.

    [2]       Alzaghal A, Hamed D. New Families of Generalized Lomax Distributions: Properties and Applications. Int J Stat Probab 2019;8:51. https://doi.org/10.5539/ijsp.v8n6p51.

    [3]       Hamed D, Alzaghal A. New class of Lindley distributions: properties and applications. J Stat Distrib Appl 2021;8. https://doi.org/10.1186/s40488-021-00127-y.

    [4]       Bensid AE, Zeghdoudi H. On the Lindley family distribution: quantile function, limiting distributions of sample minima and maxima and entropies n.d.

    [5]       Pfeiffer J. Coded Modulation for Physical-Layer Security 2023.

    [6]       Ross J V, Pagendam DE, Pollett PK. On parameter estimation in population models II: multi-dimensional processes and transient dynamics. Theor Popul Biol 2009;75:123–32.

    [7]       Alzaatreh A, Lee C, Famoye F. T-normal family of distributions: a new approach to generalize the normal distribution. J Stat Distrib Appl 2014;1:16. https://doi.org/10.1186/2195-5832-1-16.

    [8]       Ali BK, Nasr MW. Choosing the best estimate of the fuzzy reliability of the Freget distribution. Master’s thesis, University of Karbala, College of Administration and Economics., 2018.

    [9]       Neamah MW, Ali BK. Fuzzy reliability estimation for Frechet distribution by using simulation. Period Eng Nat Sci 2020;8:632–46.

    [10]     Chaira T. Fuzzy Set and Its Extension. Wiley; 2019. https://doi.org/10.1002/9781119544203.

    [11]     Yang Y, Li XR, Han D. An improved α-cut approach to transforming fuzzy membership function into basic belief assignment. Chinese J Aeronaut 2016;29:1042–51. https://doi.org/10.1016/j.cja.2016.03.007.

    [12]     Ali BK, Nimah MW. A general robust fuzzy Bayesian method for probability distributions. 2022.

    [13]     Kumar K, Kostina E. Optimal Parameter Estimation Techniques for Complex Nonlinear Systems. Differ Equations Dyn Syst 2024. https://doi.org/10.1007/s12591-024-00688-9.

    Cite This Article As :
    Najy, Shams. , Wahab, Mahdi. Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2024, pp. 01-14. DOI: https://doi.org/10.54216/GJMSA.0110201
    Najy, S. Wahab, M. (2024). Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data. Galoitica: Journal of Mathematical Structures and Applications, (), 01-14. DOI: https://doi.org/10.54216/GJMSA.0110201
    Najy, Shams. Wahab, Mahdi. Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data. Galoitica: Journal of Mathematical Structures and Applications , no. (2024): 01-14. DOI: https://doi.org/10.54216/GJMSA.0110201
    Najy, S. , Wahab, M. (2024) . Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data. Galoitica: Journal of Mathematical Structures and Applications , () , 01-14 . DOI: https://doi.org/10.54216/GJMSA.0110201
    Najy S. , Wahab M. [2024]. Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data. Galoitica: Journal of Mathematical Structures and Applications. (): 01-14. DOI: https://doi.org/10.54216/GJMSA.0110201
    Najy, S. Wahab, M. "Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 01-14, 2024. DOI: https://doi.org/10.54216/GJMSA.0110201