Future Prediction for Tax Complaints to Turkish Ombudsman by Models from Polynomial Regression and Parametric Distribution

Abstract

The aim of this study is to forecast the amount of tax complaints filed with the Turkish Ombudsman in the future and whether or not policymakers require a specific tax Ombudsman. The polynomial regression for discrete data set is proposed to fit the number of events of tax complaints in the period from years $2013$ to $2021$. The artificial data set is generated by models which are polynomial regression and parametric distribution. The location, scale and shape parameters are determined according to the smallest value between the observed and predicted dependent variable. After determining the smallest value for the tried values of shape parameter and the parameters of polynomial regression, the best value determined by grid search for shape parameter is around $1.07$. Thus, the heavy-tailed from of exponential power distribution is gained. The artificial data sets are generated and sorted from the smallest to biggest ones. The maximum values are around $700$ and $800$ which can be regarded as future prediction because the distance among observations is taken into account by models from polynomial regression and parametric distribution. Since the polynomial regression and the parametric models are used simultaneously for modelling, the distance among observations can also be modelled by parametric model as an alternative approach provided.

Keywords

• estimation
• inference
• public economics
• parametric models
• simulation

Ethical Statement

Çalışmada etik onay belgesi gerektiren bir veri kullanılmamıştır.

References

1. Alzer, H. and A. Z. Grinshpan, 2007 Inequalities for the gamma and q-gamma functions. Journal of Approximation Theory 144: 67–83.
2. Arslan, O. and A. I. Genç, 2009 The skew generalized t distribution as the scale mixture of a skew exponential power distribution and its applications in robust estimation. Statistics 43: 481–498.
3. Bala, S. K. and P. K. Biswas, 2005 Tax-ombudsman in bangladesh: an analytical review of the regulatory framework. Cost and Management 33: 27–40.
4. Balakrishnan, N. and V. B. Nevzorov, 2004 A primer on statistical distributions. John Wiley & Sons.
5. Çankaya, M. N., 2018 Asymmetric bimodal exponential power distribution on the real line. Entropy 20: 23.
6. Çankaya, M. N. and O. Arslan, 2020 On the robustness properties for maximum likelihood estimators of parameters in exponential power and generalized t distributions. Communications in Statistics-Theory and Methods 49: 607–630.
7. Çankaya, M. N., A. Yalçınkaya, Ö. Altındaˇ g, and O. Arslan, 2019 On the robustness of an epsilon skew extension for burr iii distribution on the real line. Computational Statistics 34: 1247–1273.
8. Çankaya, M. N., 2021 Derivatives by ratio principle for q-sets on the time scale calculus. Fractals 29: 2140040.

9. Coles, S., J. Bawa, L. Trenner, and P. Dorazio, 2001 An introduction to statistical modeling of extreme values, volume 208. Springer.
10. De Gregorio, J., D. Sanchez, and R. Toral, 2023 Entropy estimators for markovian sequences: A comparative analysis. arXiv preprint arXiv:2310.07547 .
11. Haberman, S. J., 1989 Concavity and estimation. The Annals of Statistics pp. 1631–1661.
12. Härdle, W., M. Müller, S. Sperlich, A.Werwatz, et al., 2004 Nonparametric and semiparametric models, volume 1. Springer.
13. Hunter, D. R., 2023 Unsupervised clustering using nonparametric finite mixture models. Wiley Interdisciplinary Reviews: Computational Statistics p. e1632.
14. Iacus, S. M. et al., 2008 Simulation and inference for stochastic differential equations: with R examples, volume 486. Springer.
15. Jenkins, S. P., 2017 Pareto models, top incomes and recent trends in uk income inequality. Economica 84: 261–289.
16. Lehmann, E. L. and G. Casella, 2006 Theory of point estimation. Springer Science & Business Media.
17. Mineo, A. and M. Ruggieri, 2005 A software tool for the exponential power distribution: The normalp package. Journal of Statistical Software 12: 1–24.
18. Mokhtari, F., R. Rouane, S. Rahmani, and M. Rachdi, 2022 Consistency results of the m-regression function estimator for stationary continuous-time and ergodic data. Stat 11: e484.
19. Montgomery, D. C., E. A. Peck, and G. G. Vining, 2021 Introduction to linear regression analysis. John Wiley & Sons.
20. Serrano, F., 2007 The taxpayer’s rights and the role of the tax ombudsman: an analysis from a spanish and comparative law perspective. Intertax 35.
21. Sicuro, G., P. Tempesta, A. Rodríguez, and C. Tsallis, 2015 On the robustness of the q-gaussian family. Annals of Physics 363: 316–336.
22. Stanimirovi´c, I., 2017 Computation of generalized matrix inverses and applications. CRC Press.
23. Vila, R., L. Alfaia, A. F. Menezes, M. N. Çankaya, and M. Bourguignon, 2022 A model for bimodal rates and proportions. Journal of Applied Statistics pp. 1–18.
24. Vila, R., L. Ferreira, H. Saulo, F. Prataviera, and E. Ortega, 2020 A bimodal gamma distribution: properties, regression model and applications. Statistics 54: 469–493.