Nevertheless, the main subject of this study is the calculation of the shortest confidence intervals for any multimodal distribution.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:The shortest interval approach can be solved as an optimization problem, while the equally tailed approach is determined by using the distribution function.
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Temel Bulgular & Veri:The equal density approach is proposed instead of the optimization problem for determining the shortest confidence interval.
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Sonuç & Katkı:Nevertheless, the main subject of this study is the calculation of the shortest confidence intervals for any multimodal distribution.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Multimodal probability density function · Confidence interval estimators · The shortest confidence interval
Abstract
The shortest interval approach can be solved as an optimization problem, while the equally tailed approach is determined by using the distribution function. The equal density approach is proposed instead of the optimization problem for determining the shortest confidence interval. It is applied to multimodal probability density functions to determine the shortest confidence interval. Furthermore, the equal density and optimization approach for the shortest confidence interval and the equally tailed approach were applied to numerical examples and their results were compared. Nevertheless, the main subject of this study is the calculation of the shortest confidence intervals for any multimodal distribution.
KESEMEN, O., TİRYAKİ, B., ÖZKUL, E., TEZEL, Ö. (2018). Determination of the Confidence Intervals for Multimodal Probability Density Functions. Gazi University Journal of Science, Cilt: 31 - Sayı: 1, 310–326. https://ajindex.com/articles/254693
J. Neyman, "Outline of a theory of statistical estimation based on the classical theory of probability," Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 236, no. 767, pp. 333-380, (1937). A. Wald, "Asymptotically shortest confidence intervals," The Annals of Mathematical Statistics, vol. 13, no. 2, pp. 127-137, (1942). C. R. Blyth and D. W. Hutchinson, "Table of Neyman-shortest unbiased confidence intervals for the binomial parameter," Biometrika, vol. 47, no. 3/4, pp. 381-391, (1960). Z. Sidak, "Rectangular confidence regions for the means of multivariate normal distributions," Journal of the American Statistical Association, vol. 62, no. 318, pp. 626-633, (1967). K. Levy and S. Narula, "Shortest confidence intervals for the ratio of two normal variances," Canadian Journal of Statistics, vol. 2, no. 1-2, pp. 83-87, (1974). T. J. DiCiccio and J. P. Romano, "A review of bootstrap confidence intervals," Journal of the Royal Statistical Society. Series B (Methodological), pp. 338-354, (1988). A. B. Owen, "Empirical likelihood ratio confidence intervals for a single functional," Biometrika, vol. 75, no. 2, pp. 237-249, (1988). K. K. Ferentinos, "Shortest confidence intervals for families of distributions involving truncation parameters," The American Statistician, vol. 44, no. 2, pp. 167-168, (1990). K. Ferentinos and S. Kourouklis, "Shortest confidence interval estimation for families of distributions involving two truncation parameters," Metrika, vol. 37, no. 1, pp. 353-363, (1990). R. Juola, "More on shortest confidence intervals," The American Statistician, vol. 47, no. 2, pp. 117-119, (1993). S. Weerahandi, "Generalized confidence intervals," in Exact Statistical Methods for Data Analysis, Springer New York, pp. 143-168, (1995). R. G. Newcombe, "Two-sided confidence intervals for the single proportion: comparison of seven methods," Statistics in medicine, vol. 17, no. 8, pp. 857-872, (1998). R. Willink, "A confidence interval and test for the mean of an asymmetric distribution," Communications in Statistics—Theory and Methods, vol. 34, no. 4, pp. 753-766, (2005). X. H. Zhou and P. Dinh, "Nonparametric confidence intervals for the one-and two-sample problems," Biostatistics, vol. 6, no. 2, pp. 187-200, (2005). G. B. Kibria, "Modified confidence intervals for the mean of the asymmetric distribution," Pak. J. Statist, vol. 22, no. 2, pp. 109-120, (2006). B. D. Burch, "Comparing equal-tail probabil