Testing the annual rainfall dispersion in Chaiyaphum, Thailand, by using confidence intervals for the coefficient of variation of an inverse gamma distribution

Wararit Panichkitkosolkul

doi:https://doi.org/10.59170/stattrans-2023-054

Testing the annual rainfall dispersion in Chaiyaphum, Thailand, by using confidence intervals for the coefficient of variation of an inverse gamma distribution

Wararit Panichkitkosolkul 1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathumthani 12120, Thailand ORCID:https://orcid.org/0000-0001-8315-8185 Statistics in Transition new series, vol. 24, 2023, 4, pages: 109-122 Published online: 8 September 2023 https://doi.org/10.59170/stattrans-2023-054 Citation: Panichkitkosolkul, W., 2023. Testing the annual rainfall dispersion in Chaiyaphum, Thailand, by using confidence intervals for the coefficient of variation of an inverse gamma distribution. Statistics in Transition new series, 24(4), pp. 109-122. https://doi.org/10.59170/stattrans-2023-054

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ABSTRACT

In Thailand, droughts are regular natural disasters that happen nearly every year due to several factors such as precipitation deficiency, human activity, and the global warming. Since annual rainfall amount fits an inverse gamma (IG) distribution, we wanted to try testing annual rainfall dispersion via the coefficient of variation (CV). Herein, we propose two statistics for testing the CV of an IG distribution based on the Score and Wald methods. We evaluated their performances by means of the Monte Carlo simulations conducted under several shape parameter values for an IG distribution based on empirical type I error rates and powers of the tests. The simulation results reveal that the Wald-method test statistic performed better than the Score-method one in terms of the attained nominal significance level, and is thus recommended for analysis in similar scenarios. Furthermore, the efficacy of the proposed test statistics was illustrated by applying them to the annual rainfall amounts in Chaiyaphum, Thailand.

KEYWORDS

statistical test, measure of dispersion, continuous distribution, simulation, meteorology

REFERENCES

Abid, S. H., Al-Hassany, S. A., (2016). On the inverted gamma distributions. International Journal of Systems Science and Applied Mathematics, Vol. 1, pp. 16–22.

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, Vol. 19, pp. 716–723.

Albatineh, A. N., Boubakari, I. and Kibra, B. M. G., (2017). New confidence interval estimator of the signal-to-noise ratio based on asymptotic sampling distribution. Communication in Statistics-Theory and Methods, Vol. 46, pp. 574–590.

Archana, V., Rao, K. A., (2011). Improved estimators of coefficient of variation in a finite population, Statistics in Transition new series, Vol. 12, pp. 357–380.

Calif, R., Soubdhan, T., (2016). On the use of the coefficient of variation to measure spatial and temporal correlation of global solar radiation. Renewable Energy, Vol. 88, pp. 192–199.

Eartheclipse, (2022). What is a Drought?. [online]. Retrieved from https://eartheclipse. com/natural-disaster/causes-and-effects-of-drought.html, 2 April 2022.

Faber, D. S., Korn, H., (1991). Applicability of the coefficient of variation method for analyzing synaptic plasticity. Biophysical Journal, Vol. 60, pp. 1288–1294.

Gaffke, N., Heiligers, B. and Offinger, H., (2002). On the asymptotic null-distribution of the Wald statistic at singular parameter points. Statistics & Decisions, Vol. 20, pp. 379–398.

Gelman, A., (2006). Prior distributions for variance parameters in hierarchical models, Bayesian Analysis, Vol. 1, pp. 515–533.

Glen, A. G., Leemis, L. M., eds. (2017). Computational Probability Applications. International Series in Operations Research & Management Science, Vol. 247, Cham: Springer.

Google Maps, (2023). Chaiyaphum, Available from: https://www.google.co.th/maps/ @16.0082727, 101.33255,9z?hl=en [Accessed 8 February 2023].

Ihaka, R., Gentleman, R., (1996). R: a language for data analysis and graphics. Journal of Computational and Graphical Statistics, Vol. 5, 299–314.

Kaewprasert, T., Niwitpong, S. A. and Niwitpong, S., (2020). Confidence interval for coefficient of variation of inverse gamma distributions, In: HUYNH, V. N., ENTANI, T., Jeenanunta, C., Inuiguchi, M., Yenradee, P. (Eds.). Lecture Notes in Artificial Intelligence: Vol.12482. Integrated Uncertainty in Knowledge Modelling and Decision Making, pp. 407–418, Cham: Springer.

Kaewprasert, T., Niwitpong, S. A. and Niwitpong, S., (2023). Confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions. Applied Science and Engineering Progress, Vol. 16, doi.org/10.14416/ j.asep.2021.12.002.

Kang, C. W., Lee, M. S., Seong, Y. J. and Hawkins, D. M., (2007). A control chart for the coefficient of variation. Journal of Quality Technology, Vol. 39, pp. 151–158.

Kay, S. M., (1993). Fundamentals of statistical signal processing: Estimation theory. Englewood Cliffs: Prentice-Hall.

Khadka, D., Babel, M. S., Shrestha, S., Virdis and S. G. P., Collins, M., (2021). Multivariate and multi-temporal analysis of meteorological drought in the northeast of Thailand. Weather and Climate Extremes, Vol. 34, https://doi. org/10.1016/j.wace.2021.100399.

Llera, S., Beckmann, C. F., (2016). Estimating an inverse gamma distribution. Technical report, Radbound University Nijmegen, Donders Institute for Brain Cognition and Behavior. ar.Xiv: 1605.01019v2.

Milevsky, M. A., Posner, S. E., (1998). Asian options, the sum of log-normals and the reciprocal gamma distribution. The Journal of Financial and Quantitative Analysis, Vol. 33, pp. 203–218.

Nationthailand, (2022). Nine hospitals in provinces suffer impact from drought, [online]. Retrieved from https://www.nationthailand.com/in-focus/30380811, 5 April 2022.

Pang, W. K., Yu, B. W. T., Troutt, M. D. and Hou, S. H., (2008). A simulation-based approach to the study of coefficient of variation of dividend yields. European Journal of Operational Research, Vol. 189, pp. 559–569.

Pattayamail, (2022). Drought situation in Chaiyaphum reaches crisis point, [online]. Retrieved from https://www.pattayamail.com/thailandnews/drought-situation-inchaiyaphum- reaches-crisis-point-260702, 5 April 2022.

Prabnakorn, S., Maskey, S., Suryadi, F. X. and de Fraiture, C., (2018). Rice yield in response to climate trends and drought index in the Mun River Basin, Thailand. Science of the Total Environment, Vol. 621, pp. 108–119.

Rao, C. R., (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 44, pp. 50–57.

Rao, C. R., (2005). Score Test: Historical Review and Recent Developments. In: Advances in Ranking and Selection, Multiple Comparisons, and Reliability. Boston: Birkhäuser, pp. 3–20.

RamÍRez-Espinosa, P. Lopez-Martinez, F. J., (2019). On the utility of the inverse gamma distribution in modeling composite fading channels. In: 2019 IEEE Global Communications Conference (GLOBECOM). Waikoloa, Hawaii, USA, 9–13 December 2019, New York: Curran Associates.

Rasheed, H. A., Sultan, A. J., (2015). Bayesian estimation of the scale parameter for inverse gamma distribution under Linex loss function. International Journal of Advanced Research, Vol. 3, pp. 369–375.

Reed, G. F., Lynn, F. and Meade, B. D. (2002). Use of coefficient of variation in assessing variability of quantitative assays. Clinical and Diagnostic Laboratory Immunology, Vol. 9, pp. 1235–1239.

Rivera, P. A., CalderÍN-Ojeda, E., Gallardo D. I. and Gómez H. W., (2021). A compound class of the inverse gamma and power series distributions. Symmetry, Vol. 13, https://doi.org/10.3390/sym13081328.

Singh, R., Mishra, M., (2019). Estimating population coefficient of variation using a single auxiliary variable in simple random sampling. Statistics in Transition new series, Vol. 20, pp. 89–111.

Srichaiwong, P., Ardwichai, S., Tungchuvong, L. and Kenpahoom, S., (2020). The live weir innovation at Chi river watershed, Chaiyaphum province, Thailand. Bioscience Biotechnology Research Communications, Vol. 13, pp. 103–107.

Thangjai, W., Niwitpong, S., (2020). Comparing particulate matter dispersion in Thailand using the Bayesian confidence intervals for ratio of coefficients of variation, Statistics in Transition new series, Vol. 21, pp. 41–60.

Wichitarapongsakun, P., Sarin, C., Klomjek, P. and Chuenchooklin, S. (2016). Rainfall prediction and meteorological drought analysis in the Sakae Krang River basin of Thailand. Agriculture and Natural Resources, Vol. 50, pp. 490–498.

Yoo, S. K., Cotton, S. L., Zhang, L. and Sofotasios, P. C., (2019). The inverse gamma distribution: a new shadowing model, In: 2019 8th Asia-Pacific Conference on Antennas and Propagation (APCAP), Incheon, Korea (South), 4–7 August 2019, pp. 475–476.

Zhang, L., Zhang, Y. Y., (2022). The Bayesian posterior and marginal densities of the hierarchical gamma–gamma, gamma–inverse gamma, inverse gamma–gamma, and inverse gamma–inverse gamma models with conjugate priors. Mathematics, Vol. 10, https://doi.org/10.3390/math10214005.