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A Modi ed Entropy-Based Goodness-of-Fit Tes for Inverse Gaussian Distribution
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 Title & Authors
A Modi ed Entropy-Based Goodness-of-Fit Tes for Inverse Gaussian Distribution
Choi, Byung-Jin;
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This paper presents a modified entropy-based test of fit for the inverse Gaussian distribution. The test is based on the entropy difference of the unknown data-generating distribution and the inverse Gaussian distribution. The entropy difference estimator used as the test statistic is obtained by employing Vasicek's sample entropy as an entropy estimator for the data-generating distribution and the uniformly minimum variance unbiased estimator as an entropy estimator for the inverse Gaussian distribution. The critical values of the test statistic empirically determined are provided in a tabular form. Monte Carlo simulations are performed to compare the proposed test with the previous entropy-based test in terms of power.
Inverse Gaussian distribution;entropy;entropy characterization;entropy estimator;entropy-based test;power;
 Cited by
Ahmed, N. A. and Gokhale, D. V. (1989). Entropy expressions and their estimators for multivariate distributions, IEEE Transactions on Information Theory, 35, 688–692. crossref(new window)

Chhikara, R. S. and Folks, J. L. (1989). The Inverse Gaussian Distribution: Theory, Methodology, and Applications, Marcel Dekker, New York.

Choi, B. (2006). Minimum variance unbiased estimation for the maximum entropy of the transformed inverse Gaussian random variable by $Y=X^{-1/2}$, The Korean Communications in Statistics, 13, 657–667. crossref(new window)

Choi, B. and Kim, K. (2006). Testing goodness-of-fit for Laplace distribution based on maximum entropy, Statistics, 40, 517–531. crossref(new window)

Cressie, N. (1976). On the logarithms of high-order spacings, Biometrika, 63, 343–355. crossref(new window)

Dudewicz, E. J. and van der Meulen, E. C. (1981). Entropy-based test for uniformity, Journal of the American Statistical Association, 76, 967–974. crossref(new window)

Edgeman, R. L. (1990). Assessing the inverse Gaussian distribution assumption, IEEE Transactions on Reliability, 39, 352–355. crossref(new window)

Edgeman, R. L., Scott, R. C. and Pavur, R. J. (1988). A modified Kolmogorov Smirnov test for the inverse density with unknown parameters, Communications in Statistics-Simulation and Computation, 17, 1203–1212. crossref(new window)

Edgeman, R. L., Scott, R. C. and Pavur, R. J. (1992). Quadratic statistics for the goodness-of-fit test for the inverse Gaussian distribution, IEEE Transactions on Reliability, 41, 118–123. crossref(new window)

Gradsbteyn, I. S. and Pyzbik, I. M. (2000). Table of Integrals, Series, and Products, Academic Press, San Diego.

Grzegorzewski, P. and Wieczorkowski, P. (1999). Entropy-based test goodness of-fit test for exponentiality, Communications in Statistics-Theory and Methods, 28, 1183–1202. crossref(new window)

Kapur, J. N. and Kesavan, H. K. (1992). Entropy Optimization Principles with Applications, Academic Press, San Diego.

Lieblein, J. and Zelen, M. (1956). Statistical investigation of the fatigue life of deep groove ball bearings, Journal of Research of the National Bureau of Standards, 57, 273–316. crossref(new window)

Michael, J. R., Schucany, W. R. and Hass, R. W. (1976). Generating random variables using transformation with multiple roots, The American Statistician, 30, 88–90. crossref(new window)

Mudholkar, G. S. and Tian, L. (2002). An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit test, Journal of Statistical Planning and Inference, 102, 211–221. crossref(new window)

O'Reilly, F. J. and Rueda, R. (1992). Goodness of fit for the inverse Gaussian distribution, The Canadian Journal of Statistics, 20, 387–397. crossref(new window)

Seshadri, V. (1999). The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer, New York.

Shannon, C. E. (1948). A mathematical theory of communications, Bell System Technical Journal, 27, 379–423, 623–656. crossref(new window)

van Es, B. (1992). Estimating functionals related to a density by a class of statistics based on spacings, Scandinavian Journal of Statistics, 19, 61–72.

Vasicek, O. (1976). A test for normality based on sample entropy, Journal of the Royal Statistical Society, B38, 54–59.