This article introduces unit Nadarajah and Haghighi distribution to deal with the inflation of ones. Besides deriving statistical properties of the proposed distribution, several estimation methods are discussed. In particular, maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squared estimation (WLSE), maximum product spacing (MPS), minimum spacing absolute distance estimation (MSADE), minimum spacing absolute log-distance estimation (MSALDE), Cram'er-Von-Mises (CVM), Anderson-Darling method (AD) and right-tail Anderson-Darling method (RAD) are considered. Using real data sets, it is shown that the new distribution outperforms some well-known existing distribution. Furthermore, the application of the proposed distribution in quality control is also discussed. A control chart using unit Nadarajah and Haghighi distribution is constructed and its performance is evaluated using the average run length.
Mazucheli, J., Menezes, A. F. B., Fernandes, L. B., de Oliveira, R. P., and Ghitany, M. E., “The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates”, Journal of Applied Statistics, 47(6), pp. 954–974 (2020).
Mazucheli, J., Menezes, A.F.B., and Dey, S., “Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution”, Communications in Statistics-Theory and Methods, 47(15), pp. 3767–3778 (2018).
Menezes, A. F. B., Mazucheli, J., and Dey, S., “The unit-logistic distribution: Different methods of estimation”, Pesquisa Operacional, 38(3), pp. 555–578 (2018). 4. Mazucheli, J., Menezes, A.F.B., and Chakraborty, S., “On the one parameter unit- Lindley distribution and its associated regression model for proportion data”, Journal of Applied Statistics, 46(4), pp. 700–714 (2019). 5. Mazucheli, J., Menezes, A.F.B., and Dey, S., “Unit-Gompertz distribution with applications”, Statistica, 79(1), pp. 25–43 (2019). 6. Sangsanit, Y. and Bodhisuwan, W., “The Topp-Leone generator of distributions: properties and inferences.”, Songklanakarin Journal of Science & Technology, 38(5) ((2016)). 7. Condino, F. and Domma, F., “A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution”, Metron, 75(1), pp. 51–68 (2017). 8. Nadarajah, S. and Haghighi, F., “An extension of the exponential distribution”, Statistics, 45(6), pp. 543–558 (2011). 9. Marshall, A.W. and Olkin, I., “Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families”. Springer Series in Statistics, Springer New York (2007). 10. Aban, I. B., Meerschaert, M. M., and Panorska, A. K., “Parameter estimation for the truncated pareto distribution”, Journal of the American Statistical Association, 101(473), pp. 270–277 (2006). 11. Zhang, T. and Xie, M., “On the upper truncated Weibull distribution and its reliability implications”, Reliability Engineering & System Safety, 96(1), pp. 194 – 200 (2011). 12. Papke, L.E. and Wooldridge, J.M., “Econometric methods for fractional response variables with an application to 401(k) plan participation rates”, Journal of Applied Econometrics, 11(6), pp. 619–632 (1996). 13. Fletcher, S.G. and Ponnambalam, K., “Estimation of reservoir yield and storage distribution using moments analysis”, Journal of Hydrology, 182(1), pp. 259 – 275 (1996). 14. Seifi, A., Ponnambalam, K., and Vlach, J., “Maximization of manufacturing yield of systems with arbitrary distributions of component values”, Annals of Operations Research, 99, p. 373–383 (2000). 15. Gangi, A., K., Ponnambalam., D., Khalili., and Karamouz, M., “Grain yield reliability analysis with crop water demand uncertainty”, Stochastic Environmental Research and Risk Assessment, 20(4), pp. 259 – 277 (2006). 16. Cook, D. O., Kieschnick, R., and McCullough, B. D., “Regression analysis of proportions in finance with self selection”, Journal of Empirical Finance, 15(5), pp. 860 – 867 (2008). 17. Genc, A.I., “Estimation of p(x > y) with Topp–Leone distribution”, Journal of Statistical Computation and Simulation, 83(2), pp. 326–339 (2013). UNH 15 18. Ali, S., Dey, S., Tahir, M.H., and Mansoor, M., “Two-parameter logistic-exponential distribution: Some new properties and estimation methods”, American Journal of Mathematical and Management Sciences, 39(3), pp. 270–298 (2020). 19. Ali, S., Dey, S., Tahir, M. H., and Mansoor, M., “A comparison of different methods of estimation for the flexible Weibull distribution”, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), pp. 794 – 814 (2020). 20. Cheng, R. C. H. and Amin, N. A. K., “Maximum product of spacings estimation with application to the lognormal distribution”, tech. rep., (1979). 21. Cheng, R. C. H. and Amin, N. A. K., “Estimating parameters in continuous univariate distributions with a shifted origin”, Journal of the Royal Statistical Society. Series B (Methodological), 45(3), pp. 394–403 (1983). 22. Torabi, H., “A general method for estimating and hypotheses testing using spacings”, Journal of Statistical Theory and Practice, 8(2), pp. 163–168 (2008). 23. MacDonald, P. D. M., “Comment on ”an estimation procedure for mixtures of distributions” by Choi and Bulgren”, Journal of the Royal Statistical Society. Series B (Methodological), 33(2), pp. 326–329 (1971). 24. Shamsuzzaman, M., Xie, X., Goh, N.T., and Zhang, H., “Integrated control chart system for time-between-events monitoring in a multistage manufacturing system”, The International Journal of Advanced Manufacturing Technology, 40(3-4), pp. 373–381 (2009). 25. Zhang, C.W., Xie, M., Liu, J.Y., and Goh, T.N., “A control chart for the gamma distribution as a model of time between events”, International Journal of Production Research, 45(23), pp. 5649–5666 (2007). 26. Ali, S., Pievatolo, A., and G¨ob, R., “An overview of control charts for high quality processes”, Quality and Reliability Engineering International, 32(7), pp. 2171–2189 (2016). 27. Linda, L. H., Fernandes, F.H., and Bourguignon, M., “Control charts to monitor rates and proportions”, Quality and Reliability Engineering International, 35(1), pp. 74–83 (2019). 28. Cruz, F. R. B., Quinino, R. C., and Ho., Linda L., “Control charts for traffic intensity monitoring of Markovian multiserver queues”, Quality and Reliability Engineering International, 36(1), pp. 354–364 (2020). 29. Lima-Filho, L. M. de A., Pereira, T.L., de Souza, T. C., and Bayer, F.M., “Inflated beta control chart for monitoring double bounded processes”, Computers & Industrial Engineering, 136, pp. 265 – 276 (2019). 30. Lima-Filho, L.M. de A. and Bayer, F. M., “Kumaraswamy control chart for monitoring double bounded environmental data”, Communications in Statistics - Simulation and Computation, 50(9), pp. 2513–2528 (2021). 31. Chukhrova, N. and Johannssen, A., “Improved control charts for fraction non-conforming based on hypergeometric distribution”, Computers & Industrial Engineering, 128, pp. 795 – 806 (2019). 32. Lemonte, A.J., “Improved point estimation for the Kumaraswamy distribution”, Journal of Statistical Computation and Simulation, 81(12), pp. 1971–1982 (2011). 33. Bourguignon, M., Ghosh, I., and Cordeiro, G.M., “General results for the transmuted family of distributions and new models”, Journal of Probability and Statistics, 2016, pp. 1–12 (2016).
Articles in Press, Accepted Manuscript Available Online from 14 November 2021
Shah, I., Iqbal, B., Farhan Akram, M., Ali, S., & Dey, S. (2021). UNIT NADARAJAH AND HAGHIGHI DISTRIBUTION: PROPERTIES AND APPLICATIONS IN QUALITY CONTROL. Scientia Iranica, (), -. doi: 10.24200/sci.2021.57302.5167
MLA
Ismail Shah; Brikhna Iqbal; Muhammad Farhan Akram; Sajid Ali; Sanku Dey. "UNIT NADARAJAH AND HAGHIGHI DISTRIBUTION: PROPERTIES AND APPLICATIONS IN QUALITY CONTROL". Scientia Iranica, , , 2021, -. doi: 10.24200/sci.2021.57302.5167
HARVARD
Shah, I., Iqbal, B., Farhan Akram, M., Ali, S., Dey, S. (2021). 'UNIT NADARAJAH AND HAGHIGHI DISTRIBUTION: PROPERTIES AND APPLICATIONS IN QUALITY CONTROL', Scientia Iranica, (), pp. -. doi: 10.24200/sci.2021.57302.5167
VANCOUVER
Shah, I., Iqbal, B., Farhan Akram, M., Ali, S., Dey, S. UNIT NADARAJAH AND HAGHIGHI DISTRIBUTION: PROPERTIES AND APPLICATIONS IN QUALITY CONTROL. Scientia Iranica, 2021; (): -. doi: 10.24200/sci.2021.57302.5167