A new asymptotic distribution-based method for testing the signal-to-noise ratio in birth weight data from Thailand. (English) Zbl 1483.62058
Summary: We can find two different asymptotic distributions for the signal-to-noice ratio (SNR) statistics in the literature. Because the limit in distribution is unique, one of them should be wrong. In this paper, we show that the derivation of the asymptotic by K. K. Sharma and H. Krishna [“Asymptotic sampling distribution of inverse coefficient-of-variation and its applications”, IEEE Trans. Reliab. 43, No. 4, 630–633 (1994; doi:10.1109/24.370217)] is erroneous. We provide a different derivation of the correct asymptotic previously derived by A. N. Albatineh et al. [Commun. Stat., Theory Methods 46, No. 2, 574–590 (2017; Zbl 1360.62064)]. Herein, we propose a method for testing the population SNR and identify an appropriate method for practitioners. We present a new asymptotic distribution based method for testing the population SNR. A simulation study is conducted under several SNR values for normal, log-normal, chi-square, and gamma distributions, to evaluate the performances of the proposed method. The performance is evaluated based on the powers of the tests. We apply our findings to the real life problem of the estimation of the data for birth weight in Thailand, one of the main indicators of maternal and fetal health and nutrition status. Usually, such data are analysed based on the fact of their fitting a normal distribution. However, some situations have led us to consider testing infant birth weight data in terms of the signal-to-noise ratio.
MSC:
| 62F03 | Parametric hypothesis testing |
| 62D05 | Sampling theory, sample surveys |
| 62E20 | Asymptotic distribution theory in statistics |
| 62F25 | Parametric tolerance and confidence regions |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Citations:
Zbl 1360.62064References:
| [1] | Pearson, K., Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia, Phil. Trans. R. Soc. London, Ser. A, 187, 253-318 (1896) · JFM 27.0185.01 · doi:10.1098/rsta.1896.0007 |
| [2] | Panichkitkosolkul, W., Improved confidence intervals for a coefficient of variation of a normal distribution, Thai. Stat., 7, 193-199 (2009) · Zbl 1364.62073 |
| [3] | Vangel, M. G., Confidence intervals for a normal coefficient of variation, Am. Stat., 50, 21-26 (1996) |
| [4] | Acharya, T.; Ray, A. K., Image Processing: Principles and Applications (2005), Hoboken: Wiley, Hoboken · doi:10.1002/0471745790 |
| [5] | Rafael, C. G.; Richard, E. W., Digital Image Processing (2008), Upper Saddle River: Prentice Hall, Upper Saddle River |
| [6] | Russ, C. J., The Image Processing Handbook (2011), Boca Raton: CRC, Boca Raton · Zbl 1216.68327 |
| [7] | Tania, S., Image Fusion: Algorithms and Applications (2008), San Diego: Academic, San Diego |
| [8] | Kapur, K.; Chen, G., Signal-to-noise ratio development for quality engineering, Qual. Reliab. Eng. Int., 4, 133-141 (1988) · doi:10.1002/qre.4680040208 |
| [9] | Kaufman, L.; Kramer, D. M.; Crooks, L. E.; Ortendahl, D. A., Measuring signal-to-noise ratios in MR imaging, Radiology, 173, 265-267 (1989) · doi:10.1148/radiology.173.1.2781018 |
| [10] | McGibney, G.; Smith, M. R., An unbiased signal-to-noise ratio measure for magnetic resonance images, Med. Phys., 20, 1077-1079 (1993) · doi:10.1118/1.597004 |
| [11] | Firbank, M. J.; Coulthard, A.; Harrison, R. M.; Williams, E. D., A comparison of two methods for measuring the signal to noise ratio on MR images, Phys. Med. Biol., 44, 261-264 (1999) · doi:10.1088/0031-9155/44/12/403 |
| [12] | Czanner, G.; Sarma, S. V.; Ba, D.; Eden, U. T.; Wu, W.; Eskandar, E.; Lim, H. H.; Temereanca, S.; Suzuki, W. A.; Brown, E. N., Measuring the signal-to-noise ratio of a neuron, Natl. Acad. Sci., 112, 7141-7146 (2015) · doi:10.1073/pnas.1505545112 |
| [13] | Patil, A. N.; Hublikar, S. P.; Faria, L. S.; Khadilkar, S. S., Improving service quality of hotel business using collective QFD and signal to noise ratio, OmniSci, 9, 34-41 (2019) |
| [14] | Liu, S. T., A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio, Ann. Oper. Res., 261, 207-232 (2018) · Zbl 1408.90150 · doi:10.1007/s10479-017-2562-8 |
| [15] | Sharma, K. K.; Krishna, H., Asymptotic sampling distribution of inverse coefficient of variation and its applications, IEEE Trans. Reliab., 43, 630-633 (1994) · doi:10.1109/24.370217 |
| [16] | George, F.; Kibria, B. M. G., Confidence intervals for signal to noise ratio of a Poisson distribution, Am. J. Biostat., 2, 44-55 (2011) |
| [17] | George, F.; Kibria, B. M. G., Confidence intervals for estimating the population signal-to-noise ratio: A simulation study, J. Appl. Stat., 39, 1225-1240 (2012) · Zbl 1514.62053 · doi:10.1080/02664763.2011.644527 |
| [18] | Albatineh, A. N.; George, F.; Kibria, B. M. G.; Wilcox, M. L., Confidence interval estimation of the signal-to-noise ratio using ranked set sampling: A simulation study, Thai. Stat., 12, 55-69 (2014) · Zbl 1365.62022 |
| [19] | Saothayanun, L.; Thangjai, W., Studies in Computational Intelligence (2018), Cham, Switzerland: Springer, Cham, Switzerland |
| [20] | Thangjai, W.; Niwitpong, S., Confidence intervals for the signal-to-noise ratio and difference of signal-to-noise ratios of log-normal distributions, Stats, 2, 164-173 (2019) · doi:10.3390/stats2010012 |
| [21] | Kibria, B. M. G.; George, F., Methods for testing population signal-to-noise ratio, Commun. Stat. Simul. Comput., 43, 443-461 (2014) · Zbl 1291.62053 · doi:10.1080/03610918.2012.704541 |
| [22] | Albatineh, A. N.; Boubakari, I.; Kibria, B. M. G., New confidence interval estimator of the signal-to-noise ratio based on asymptotic sampling distribution, Commun. Stat. Theor. Methods, 46, 574-590 (2017) · Zbl 1360.62064 · doi:10.1080/03610926.2014.1000498 |
| [23] | Aung, E. E.; Makka, N.; Bundhamchareon, K., Estimated burden of premature death and morbidity from low birth weight infants in Thailand, Int. J. Trop. Dis. Health, 31, 1-10 (2018) · doi:10.9734/IJTDH/2018/41821 |
| [24] | Low Birthweight: Country, Regional, and Global Estimates. https://apps.who.int/iris/handle/10665/43184. Accessed 2021. |
| [25] | Newborns: Improving Survival and Well-Being. https://www.who.int/news-room/fact-sheets/detail/newborns-reducing-mortality. Accessed 2021. |
| [26] | Aarnoudse-Moens, C. S. H.; Weisglas-Kuperus, N.; van Goudoever, J. B.; Oosterlaan, J., Meta-analysis of neurobehavioral outcomes in very preterm and/or very low birth weight children, Pediatrics, 124, 717-728 (2009) · doi:10.1542/peds.2008-2816 |
| [27] | Hack, M.; Horbar, J. D.; Malloy, M. H.; Wright, L.; Tyson, J. E.; Wright, E., Very low birth weight outcomes of the National Institute of Child Health and Human Development neonatal network, Pediatrics, 87, 587-597 (1991) · doi:10.1542/peds.87.5.587 |
| [28] | Harmon, H. M.; Taylor, H. G.; Minich, N.; Wilson-Costello, D.; Hack, M., Early school outcomes for extremely preterm infants with transient neurological abnormalities, Dev. Med. Child Neurol., 57, 865-871 (2015) · doi:10.1111/dmcn.12811 |
| [29] | Child Nutrition. https://data.unicef.org/topic/nutrition/child-nutrition. Accessed 2021. |
| [30] | UNICEF-WHO Low Birthweight Estimates: Levels and Trends 2000-2015. https://data.unicef.org/resources/unicef-who-low-birthweight-estimates-levels-and-trends-2000-2015. Accessed 2021. |
| [31] | Chanvitan, P.; Ruangnapa, K.; Janjindamai, W.; Disaneevate, S., Outcomes of very low birth weight infants in Songklanagarind Hospital, J. Med. Assoc. Thai., 93, 191-198 (2010) |
| [32] | Sangtawesin, V.; Singarj, Y.; Kanjanapattanakul, W., Growth and development of very low birth weight infants aged 18-24 months at Queen Sirikit National Institute of Child Health, J. Med. Assoc. Thai., 94, 101-106 (2011) |
| [33] | National Statistical Office and United Nations Children’s Fund, Thailand Multiple Indicator Cluster Survey 2012 (2012), Bangkok, Thailand: NSO and UNICEF, Bangkok, Thailand |
| [34] | National Statistical Office and United Nations Children’s Fund, Thailand Multiple Indicator Cluster Survey 2015-2016 (2016), Bangkok, Thailand: NSO and UNICEF, Bangkok, Thailand |
| [35] | Almond, D.; Chay, K. Y.; Lee, D. S., The costs of low birth weight, Q. J. Econ., 120, 1031-1083 (2005) |
| [36] | Tongo, O.; Orimadegun, A.; Ajayi, S.; Akinyinka, O., The economic burden of preterm/very low birth weight care in Nigeria, J. Trop. Pediatr., 55, 262-264 (2008) · doi:10.1093/tropej/fmn107 |
| [37] | Lehmann, E. L., Elements of Large-Sample Theory (2004), New York: Springer Science, New York |
| [38] | S. Saad, ‘‘Asymptotic analysis of method of moments estimators of parameters \(p\) and \(m\) for the binomial distribution,’’ Ph. D. Thesis (Univ. of Regina, 2019). https:// ourspace.uregina.ca/bitstream/handle/10294/8840/SAAD_Salma_PhD_STATS_Spring2019.pdf. Accessed 2021. |
| [39] | Saad, S., Joint normality of the sample mean and sample variance, J. Prob. Stat. Sci., 17, 239-242 (2019) |
| [40] | Ihaka, R.; Gentleman, R. R., A language for data analysis and graphics, J. Comput. Graph. Stat., 5, 299-314 (1996) |
| [41] | Banik, S.; Kibria, B. M. G., Estimating the population coefficient of variation by confidence intervals, Commun. Stat. Simul. Comput., 40, 1236-1261 (2011) · Zbl 1271.62050 · doi:10.1080/03610918.2011.568151 |
| [42] | McKenzie, J. D., Minitab Student Release 14: Statistical Software for Education (2004), Boston: Pearson Addison-Wesley, Boston |
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