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Hypothesis testing for the mean of inverse Gaussian distribution using \(\alpha \)-cuts. (English) Zbl 1349.62090

Summary: In this study, we modify the method proposed by Buckley to testing statistical hypothesis for the mean of an inverse Gaussian distribution. In order to obtain fuzzy test statistic, we use confidence intervals by the help of \(\alpha \)-cuts. Then the method is applied to test the hypothesis for the mean of inverse Gaussian distribution when the scale parameter is known. Also a comparison is made between the fuzzy and non-fuzzy test procedure for the inverse Gaussian distribution.

MSC:

62F86 Parametric inference and fuzziness
62F03 Parametric hypothesis testing
62F25 Parametric tolerance and confidence regions

Software:

Maple
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Full Text: DOI

References:

[1] Buckley JJ (2005) Fuzzy statistics: hypothesis testing. Soft. Comput. 9:512-518 · Zbl 1079.62026
[2] Buckley JJ (2006) Fuzzy probability and statistics. Springer, Heidelberg · Zbl 1095.62002
[3] Chhikara RS, Folks JL (1989) The inverse Gaussian distribution: theory, methodology and applications. Marcel Dekker Inc., New York · Zbl 0701.62009
[4] Falsafin A, Taheri SM, Mashinchi M (2008) Fuzzy estimation of parameters in statistical models. Int. J. Comput. Math. Sci. 2:79-85 · Zbl 1186.62042
[5] Hryniewicz O (2006) Possibilistic decisions and fuzzy statistical tests. Fuzzy Sets Syst. 157:2665-2673 · Zbl 1099.62008
[6] Maple 10, Waterloo Maple Inc., Waterloo, Canada, 2005 · Zbl 1114.68629
[7] Moore, R.E.: Methods and applications of interval analysis, SIAM studies in applied mathematics. Philadeplhia, (1979) · Zbl 0417.65022
[8] Taheri SM, Arefi M (2009) Testing fuzzy hypotheses based on fuzzy test statistics. Soft. Comput. 13:617-625 · Zbl 1170.62016
[9] Zadeh LA (1965) Fuzzy sets. Inf. Control 8:338-353 · Zbl 0139.24606
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