### Confidence Interval for the Difference Between Variances of Delta-Gamma Distribution

#### Abstract

*δ*), the confidence intervals based on FQ and HPD with either the Jeffrey’s or uniform priors are suitable whereas for large

*δ*, the HPD with the normal-gamma-beta prior is recommended. Rainfall data from Lamphun province, Thailand, are used to illustrate the practical efficacies of the proposed methods.

#### Keywords

[1] J. Aitchison, “On the distribution of a positive random variable having a discrete probability mass at the origin,” Journal of the American Statistical Association, vol. 50, no. 271, pp. 901– 908, Sep. 1955.

[2] J. Aitchison and J. A. C. Brown, The lognormal distribution: With special reference to its uses in economics London. UK: Cambridge University Press, 1963.

[3] N. Yosboonruang, S. A. Niwitpong, and S. Niwitpong, “Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: A study from Thailand,” PeerJ, vol. 7, 2019, Art. no. e7344.

[4] P. Maneerat and S. A. Niwitpong, “Estimating the average daily rainfall in Thailand using confidence intervals for the common mean of several delta-lognormal distributions,” PeerJ, vol. 9, 2021, Art. no. e10758.

[5] K. Krishnamoorthy and X. Wang, “Fiducial confidence limits and prediction limits for a gamma distribution: Censored and uncensored cases,” Environmetrics, vol. 27, no. 8, pp. 479– 493, 2016.

[6] P. Ren, G. Liu, and X. Pu, “Simultaneous confidence intervals for mean differences of multiple zeroinflated gamma distributions with applications to precipitation,” Communications in Statistics - Simulation and Computation, 2021, doi: 10.1080/03610918.2021.1966466.

[7] K. Muralidharan and B. K. Kale, “Modified gamma distributions with singularity at zero,” Communications in Statistics - Simulation and Computation, vol. 31, no. 1, pp. 143–158, 2002.

[8] J. B. Lecomte, H. P. Benot, S. Ancelet, M. P. Etienne, L. Bel, and E. Parent, “Compound Poissongamma vs. delta-gamma to handle zero-inflated continuous data under a variable sampling volume,” Methods in Ecology and Evolution, vol. 4, no. 12, pp. 1159–1166, 2013.

[9] G. Casella and R. L. Berger, Statistical Inference, 2nd ed. Massachusetts: Cengage Learning, 2001

[10] K. Krishnamoorthy, T. Mathew, and S. Mukherjee, “Normal-based methods for a gamma distribution,” Technometrics, vol. 50, no. 1, pp. 69–78, 2008.

[11] X. Li, X. Zhou, and L. Tian, “Interval estimation for the mean of lognormal data with excess zeros,” Statistics Probability Letters, vol. 83, no. 11, pp. 2447–2453, 2013.

[12] P. Maneerat, S. A. Niwitpong, and S. Niwitpong, “Bayesian confidence intervals for the difference between variances of deltalognormal distributions,” Biometrical Journal, vol. 62, no. 7, pp. 1769– 1790, 2020.

[13] W. M. Bolstad and J. M. Curran, Introduction to Bayesian Statistics, 3rd ed. New Jersey: Wiley, 2016.

[14] T. A. Kalkur and A. Rao, “Bayes estimator for coefficient of variation and inverse coefficient of variation for the normal distribution,” International Journal of Statistics and Systems, vol. 12, no. 4, pp. 721–732, 2017.

[15] P. Sangnawakij, S. A. Niwitpong, and S. Niwitpong, “Confidence intervals for the ratio of coefficients of variation of the gamma distributions,” in Lecture Notes in Computer Science. Cham: Springer, 2015.

[16] M. M. A. Ananda, O. Dag, and S. Weerahandi, “Heteroscedastic two-way ANOVA under constraints,” Communications in Statistics - Theory and Methods, pp. 1–16, 2022, doi: 10.1080/ 03610926.2022.2059682.

DOI: 10.14416/j.asep.2022.12.001

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