Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data

Usanee Janthasuwan; Suparat Niwitpong; Sa-Aat Niwitpong; Usanee Janthasuwan; Suparat Niwitpong; Sa-Aat Niwitpong

doi:10.3934/math.20241631

AIMS Mathematics

2024, Volume 9, Issue 12: 34248-34269. doi: 10.3934/math.20241631

Previous Article Next Article

Research article Special Issues

Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data

Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 23 September 2024 Revised: 22 November 2024 Accepted: 25 November 2024 Published: 04 December 2024
MSC : 62F25, 62P12

The delta-Birnbaum-Saunders distribution is considered a relatively new distribution that combines the Birnbaum-Saunders distribution with data that include zero values. Furthermore, the coefficient of variation is important because it provides a standardized measure of relative variability that can be calculated from the ratio of the standard deviation to the mean. Consequently, this study focuses on constructing confidence intervals for the coefficient of variation of the delta-Birnbaum-Saunders distribution. We have proposed three methods for constructing confidence intervals: the generalized confidence interval based on the variance-stabilized transformation, the generalized confidence interval based on the Wilson score method, and the normal approximation compared with the bootstrap confidence interval. The performance of all these methods was compared using coverage probabilities and expected lengths through Monte Carlo simulations using the R statistical software, and various parameters were comprehensively specified. The study results revealed that the generalized confidence interval based on the variance stabilized transformation and the generalized confidence interval based on the Wilson score method provided similar results and were the best-performing methods. Additionally, the study results show that as the sample size increases, all methods tend to become more effective. Finally, we applied all the methods presented to wind speed data from Ubon Ratchathani province and Si Sa Kat province in Thailand.
- bootstrap confidence interval,
- coefficient of variation,
- delta-Birnbaum-Saunders,
- generalized confidence interval,
- normal approximation
Citation: Usanee Janthasuwan, Suparat Niwitpong, Sa-Aat Niwitpong. Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data[J]. AIMS Mathematics, 2024, 9(12): 34248-34269. doi: 10.3934/math.20241631

Related Papers:

Abstract

The delta-Birnbaum-Saunders distribution is considered a relatively new distribution that combines the Birnbaum-Saunders distribution with data that include zero values. Furthermore, the coefficient of variation is important because it provides a standardized measure of relative variability that can be calculated from the ratio of the standard deviation to the mean. Consequently, this study focuses on constructing confidence intervals for the coefficient of variation of the delta-Birnbaum-Saunders distribution. We have proposed three methods for constructing confidence intervals: the generalized confidence interval based on the variance-stabilized transformation, the generalized confidence interval based on the Wilson score method, and the normal approximation compared with the bootstrap confidence interval. The performance of all these methods was compared using coverage probabilities and expected lengths through Monte Carlo simulations using the R statistical software, and various parameters were comprehensively specified. The study results revealed that the generalized confidence interval based on the variance stabilized transformation and the generalized confidence interval based on the Wilson score method provided similar results and were the best-performing methods. Additionally, the study results show that as the sample size increases, all methods tend to become more effective. Finally, we applied all the methods presented to wind speed data from Ubon Ratchathani province and Si Sa Kat province in Thailand.

References

[1]	K. Mohammadi, O. Alavi, J. G. McGowan, Use of Birnbaum-Saunders distribution for estimating wind speed and wind power probability distributions: A review, Energ. Convers. Manage., 143 (2017), 109–122. https://doi.org/10.1016/j.enconman.2017.03.083 doi: 10.1016/j.enconman.2017.03.083
[2]	X. Jin, J. Kawczak, Birnbaum-Saunders and lognormal kernel estimators for modelling durations in high frequency financial data, Ann. Econ. Financ., 4 (2003), 103–124.
[3]	V. Leiva, E. Athayde, C. Azevedo, C. Marchant, Modeling wind energy flux by a Birnbaum-Saunders distribution with an unknown shift parameter, J. Appl. Stat., 38 (2011), 2819–2838. https://doi.org/10.1080/02664763.2011.570319 doi: 10.1080/02664763.2011.570319
[4]	H. Saulo, V. Leiva, F. A. Ziegelmann, C. Marchant, A nonparametric method for estimating asymmetric densities based on skewed Birnbaum-Saunders distributions applied to environmental data, Stoch. Environ. Res. Risk Assess., 27 (2013), 1479–1491. https://doi.org/10.1007/s00477-012-0684-8 doi: 10.1007/s00477-012-0684-8
[5]	J. Leão, V. Leiva, H. Saulo, V. Tomazella, Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data, Biom. J., 59 (2017), 291–314. https://doi.org/10.1002/bimj.201600008 doi: 10.1002/bimj.201600008
[6]	J. Aitchison, On the distribution of a positive random variable having a discrete probability mass at the origin, J. Am. Stat. Assoc., 50 (1955), 901–908. https://doi.org/10.1080/01621459.1955.10501976 doi: 10.1080/01621459.1955.10501976
[7]	M. S. Hasan, K. Krishnamoorthy, Confidence intervals for the mean and a percentile based on zero-inflated lognormal data, J. Stat. Comput. Simul., 88 (2018), 1499–1514. https://doi.org/10.1080/00949655.2018.1439033 doi: 10.1080/00949655.2018.1439033
[8]	P. Maneerat, S. Niwitpong, S. A. Niwitpong, Bayesian confidence intervals for the difference between variances of delta‐lognormal distributions, Biom. J., 62 (2020), 1769–1790. https://doi.org/10.1002/bimj.201900079 doi: 10.1002/bimj.201900079
[9]	L. Singhasomboon, W. Panichkitkosolkul, A. Volodin, Confidence intervals for the ratio of medians of two independent log-normal distributions, Commun. Stat. Simul. Comput., 51 (2022), 6729–6738. https://doi.org/10.1080/03610918.2020.1812649 doi: 10.1080/03610918.2020.1812649
[10]	N. Ratasukharom, S. A. Niwitpong, S. Niwitpong, Estimation methods for the variance of Birnbaum-Saunders distribution containing zero values with application to wind speed data in Thailand, PeerJ, 12 (2024), e18272. https://doi.org/10.7717/peerj.18272 doi: 10.7717/peerj.18272
[11]	H. Guo, Y. Qian, Y. Zhu, X. Dai, X. Wang, Confidence intervals for the difference between coefficients of variation of zero-inflated gamma distributions, AIMS Math., 8 (2023), 29713–29733. https://doi.org/10.3934/math.20231521 doi: 10.3934/math.20231521
[12]	W. Khooriphan, S. A. Niwitpong, S. Niwitpong, Confidence Intervals for Mean of Delta Two-Parameter Exponential Distribution, In: Integrated uncertainty in knowledge modelling and decision making, Cham: Springer, 2022. https://doi.org/10.1007/978-3-030-98018-4_10
[13]	O. Shechtman, The coefficient of variation as an index of measurement reliability. In: Methods of clinical epidemiology, Heidelberg: Springer Berlin Heidelberg, 2013. https://doi.org/10.1007/978-3-642-37131-8_4
[14]	J. G. D'Cunha, K. A. Rao, Bayesian inference for volatility of stock prices, J. Mod. Appl. Stat. Meth., 13 (2014), 29. https://doi.org/10.22237/jmasm/1414816080 doi: 10.22237/jmasm/1414816080
[15]	Z., Jalilibal, A., Amiri, P., Castagliola, M. B. Khoo, Monitoring the coefficient of variation: A literature review, Comput. Ind. Eng., 161 (2021), 107600. https://doi.org/10.1016/j.cie.2021.107600 doi: 10.1016/j.cie.2021.107600
[16]	M. G. Vangel, Confidence intervals for a normal coefficient of variation, Am. Stat., 50 (1996), 21–26. https://doi.org/10.2307/2685039 doi: 10.2307/2685039
[17]	N. Buntao, S. A. Niwitpong, Confidence intervals for the difference of coefficients of variation for lognormal distributions and delta-lognormal distributions, Appl. Math. Sci., 6 (2012), 6691–6704.
[18]	P. Sangnawakij, S. A. Niwitpong, Confidence intervals for coefficients of variation in two-parameter exponential distributions, Commun. Stat. Simul. Comput., 46 (2017), 6618–6630. https://doi.org/10.1080/03610918.2016.1208236 doi: 10.1080/03610918.2016.1208236
[19]	N. Yosboonruang, S. A. Niwitpong, S. Niwitpong, The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand, PeerJ, 8 (2020), e9662. https://doi.org/10.7717/peerj.9662 doi: 10.7717/peerj.9662
[20]	W. Puggard, S. A. Niwitpong, S. Niwitpong, Bayesian estimation for the coefficients of variation of Birnbaum-Saunders distributions, Symmetry, 13 (2021), 2130. https://doi.org/10.3390/sym13112130 doi: 10.3390/sym13112130
[21]	M. La-ongkaew, S. A. Niwitpong, S. Niwitpong, Estimation of the confidence interval for the ratio of the coefficients of variation of two Weibull distributions and its application to wind speed data, Symmetry, 15 (2022), 46. https://doi.org/10.3390/sym15010046 doi: 10.3390/sym15010046
[22]	W. H. Wu, H. N. Hsieh, Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data, J. Appl. Stat., 41 (2014), 1471–1485. https://doi.org/10.1080/02664763.2014.881780 doi: 10.1080/02664763.2014.881780
[23]	X. Li, X. Zhou, L. Tian, Interval estimation for the mean of lognormal data with excess zeros, Stat. Probab. Lett., 83 (2013), 2447–2453. https://doi.org/10.1016/j.spl.2013.07.004 doi: 10.1016/j.spl.2013.07.004
[24]	H. K. T. Ng, D. Kundu, N. Balakrishnan, Modified moment estimation for the two-parameter Birnbaum-Saunders distribution, Comput. Stat. Data Anal., 43 (2003), 283–298. https://doi.org/10.1016/S0167-9473(02)00254-2 doi: 10.1016/S0167-9473(02)00254-2
[25]	S. Weerahandi, Generalized confidence intervals, J. Am. Stat. Assoc., 88 (1993), 899–905. https://doi.org/10.1080/01621459.1993.10476355 doi: 10.1080/01621459.1993.10476355
[26]	Z. I. Sun, The confidence intervals for the scale parameter of the Birnbaum-Saunders fatigue life distribution, Acta Armamentarii, 30 (2009), 1558.
[27]	B. Efron, Bootstrap methods: another look at the jackknife, Ann. Statist., 7 (1979), 1–26. https://doi.org/10.1214/aos/1176344552 doi: 10.1214/aos/1176344552
[28]	J. G. MacKinnon, A. A. Smith Jr, Approximate bias correction in econometrics, J. Econometrics, 85 (1998), 205–230. https://doi.org/10.1016/S0304-4076(97)00099-7 doi: 10.1016/S0304-4076(97)00099-7
[29]	L. D. Brown, T. T. Cai, A. DasGupta, Interval estimation for a binomial proportion, Stat. Sci., 16 (2001), 101–133. https://doi.org/10.1214/ss/1009213286 doi: 10.1214/ss/1009213286

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)