Abstract
Different types of statistical methods are useful in data analysis in the field of science, engineering, medical, etc. In this paper, we have considered a statistical data analysis and estimation of the data by using size biased Borel–Tanner distribution. At the time of classification and analysis, there may arise error, like an observation may be misclassified into different classes or groups. Such type of data is known as misclassified data. Also, when sample units are selected with a probability proportional to the size of the units, the resultant distribution is known as a size biased distribution or weighted distributions. In this paper, we have studied misclassified size biased Borel–Tanner distribution and estimated its parameters by applying the method of maximum likelihood, method of moment, and Bayes’ estimation method. Simulation study has been carried out for comparing the three methods of estimation.
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References
Borel, E. (1942). Sur l’emploi du theoreme de Bernoulli pour faciliter le calcul d’un infinite de coefficients. Application au probleme de l’ attente a un guichet, comptes rendus. Acedemic des Sciences, Paris, Series A, 214, 452–456.
Box, G. E. P., & Tioa, G. C. (1973). Bayesian inference in statistical analysis. Wiley.
Bross, I. D. J. (1954). Misclassification in 2 × 2 tables. Biometrics, 10, 478–486.
Diamond, E. L., & Lilienfeld, A. M. (1962). Effect of errors in classification and diagnosis in various types of epidemiological studies. American Journal of Public Health, 52(7), 1137–1144.
Fisher, R. A. (1934). The effects of methods of ascertainments upon the estimation of frequencies. Annals of Eugenics, 6, 13–25.
Haight, F. A., & Breuer, M. A. (1960). The Borel–Tanner distribution. Biometrika, 47, 143–150.
Lindley, D. V. (1980). Approximate Bayes method. Trabajos de Estadistica, 31, 223–237.
Nirei, M., Stamatiou, T., & Sushko, V. (2012). Stochastic herding in financial markets evidence from institutional investor equity portfolios. BIS Working Papers, No. 371.
Parikh, N. T., & Shah, S. M. (1969). Misclassification in power series distribution in which the value one is sometimes reported as zero. Journal of Indian Statistical Association, 7, 11–19.
Patil, G. P. (2002). Weighted distributions. Encyclopedia of Environmetrics, 4, 2369–2377.
Press, S. J. (1989). Bayesian statistics: Principles, models and applications. Wiley.
Shy, C. M., Kleinbaum, D. G., & Morgenstern, H. (1978). The effect of misclassification of exposure status in epidemiological studies of air pollution health effects. Journal of Urban Health, Springer, 54(11), 1155–1165.
Tanner, J. C. (1953). A problem of interference between two queues. Biometrika, 40, 58–69.
Trivedi, B. S., & Patel, M. N. (2013). Estimation in misclassified size-biased generalized negative binomial distribution. Mathematics and Statistics, Horizon Research (Publishing Corporation), CA, USA, 1(2), 74–85.
Trivedi, B. S., & Patel, M. N. (2015). Estimation in misclassified size-biased log series distribution. Mathematical Theory and Modelling, IISTE—International Knowledge sharing Platform, USA, 5(2), 128–135.
Trivedi, B. S., & Patel, M. N. (2015). Estimation of parameters of misclassified size biased Borel distribution. Journal of Modern Applied Statistical Methods (JMASM), Wayne State University, Detroit, Michigan, USA, 15(2), 475–494.
Trivedi, B. S., & Patel, M. N. (2017). Estimation of parameters of misclassified size biased discrete lindley distribution. Communications in Statistics—Simulation and Computation, Taylor and Francis Group, UK, 45(7), 5541–5552.
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Trivedi, B.S., Patel, M.N. (2019). Estimation of Parameters of Misclassified Size Biased Borel Tanner Distribution. In: Laha, A. (eds) Advances in Analytics and Applications. Springer Proceedings in Business and Economics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1208-3_19
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DOI: https://doi.org/10.1007/978-981-13-1208-3_19
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