Double Truncated Lomax-Rayleigh Distribution and its Application
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Abstract
In this research article, the Lomax-Rayleigh distribution (LRD) is developed by truncating both sides along with the presentation of some statistical properties such as the survival function, hazard function, moment, and parameter estimation. In terms of numerical experiments, the quantile function is studied as being used to create a random variable corresponding to a TLRD distribution. The results show that the standard error (SE) of the parameter estimation decreases as the sample size n increases. To study the efficiency of the distribution, the developed distribution is applied to the five real datasets, which are the lifetime of electronic devices and medical information. The goodness-of-fit test is used for the performance comparison. The results reveal that the truncated Lomax-Rayleigh distribution is the one that is consistent with all five real datasets.
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เนื้อหาและข้อมูลในบทความที่ลงตีพิมพ์ในวารสารวิชาการปทุมวันถือเป็นข้อคิดเห็นและความรับผิดชอบของผู้เขียนบทความโดยตรง ซึ่งกองบรรณาธิการวารสารไม่จำเป็นต้องเห็นด้วยหรือร่วมรับผิดชอบใดๆ
บทความ ข้อมูล เนื้อหา ฯลฯ ที่ได้รับการตีพิมพ์ในวารสารวิชาการปทุมวันถือเป็นลิขสิทธิ์ของวารสารวิชาการปทุมวัน หากบุคคลหรือหน่วยงานใดต้องการนำทั้งหมดหรือส่วนหนึ่งส่วนใดไปเผยแพร่ต่อหรือเพื่อกระทำการใดๆ จะต้องได้รับอนุญาตเป็นลายลักษณ์อักษรจากวารสารวิชาการปทุมวันก่อนเท่านั้น
References
Lindley, D. V. (1958). Fiducial Distributions and Bayes’ Theorem. Journal of the Royal Statistical Society,
Series B, 20(1), 102-107.
Shanker, R., et al. (2013). A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data. Applied Mathematics, 4, 363-368.
Shanker, R. (2015). Akash Distribution and its Application. International Journal of Probability and Statistics, 4(3), 65–75.
Chankham, W., et al. (2022). Measurement of Dispersion of PM 2.5 in Thailand using Confidence Intervals
for the Coefficient of Variation of an Inverse Gaussian Distribution. PeerJ, 10, e12988.
Lomax, K. S. (1954). Business Failures: Another Example of the Analysis of Failure Data. Journal of the American Statistical Association, 49, 847-852.
Rayleigh, L. (1896). The Theory of Sound, Volume 2. New York: Dover Publications.
Venegas, O., et al. (2019). Lomax-Rayleigh Distribution with an Application. Applied Mathematics & Information Sciences, 13(5), 741-748.
Falgore, J. Y., et al. (2021). Inverse Lomax-Rayleigh Distribution with Application. Heliyon, 7(11), E08383.
El-Hadidya, M. A. A. & Alfreedia, A. A. (2019). Internal Truncated Distributions: Applications to Wiener Process Range Distribution when Deleting a Minimum Stochastic Volatility Interval from its Domain. Journal of Taibah University for Science, 13 (1), 201–215.
Johnson, A. C. (2001). On The Truncated Normal Distribution: Characteristics of Singly-And Doubly-
Truncated Populations of Application in Management Science, (Ph.D. Dissertation, Illinois Institute of Technology).
Iwueze, S. (2007). Some Implications of Truncating the N (1, σ2) Distribution to the Left at Zero. Journal of Applied Sciences, 7(2), 189-195.
Aryuyuen, S. (2018). Truncated Two-Parameter Lindley Distribution and its Application. The Journal of Applied Science, 17(1), 19-32.
Shukla, K. K. & Shanker, R. (2020). Truncated Akash Distribution: Properties and Applications. Biometrics &
Biostatistics International Journal, 9(5), 179-184.
Hammood, H. K., et al. (2023). Truncated Rayleigh Lomax Distribution. International Journal of Engineering Research & Technology, 12(1), 196-210.
Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. Oxford: The Oxford University Press.
Aryuyuen, S. & Bodhisuwan, W. (2019). The Truncated Power Lomax Distribution: Properties and Applications. Walailak Journal of Science and Technology, 16(9), 655-668.
Linhart, H. & Zucchini, W. (1986). Model Selection. New York: John Wiley.
Efron, B. (1988). Logistic Regression, Survival Analysis and the Kaplan-Meier Curve. Journal of the American Statistical Association, 83(402), 414-425.
Loukopoulos, P., et al. (2017). Reciprocating Compressor Prognostics of an Instantaneous Failure Mode Utilising Temperature Only Measurements. Applied Acoustics, 147, 77-86.
Zeydan, E. (2019). Hard Drive Failure Data. Available from https://www.kaggle.com/datasets/ezeydan/ hard-drive-failure-data?resource=download. Accessed date: 18 August 2023.
Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, 19, 716–723.