Volume 11 • Issue 2 • PP: 01-14 • 2024
Proposing Triple fuzzy distribution based on the Quantile Function for monotonically decreasing failure data
View PDF 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
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
Choose your preferred format