Asymptotic Confidence Ellipses for Length-biased Inverse Gaussian Distribution
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Published:
Apr 18, 2019
Keywords:
Length-biased Inverse Gaussian Distribution Fisher Information Matrix Asymptotic Confidence Ellipses
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Abstract
The length-biased inverse Gaussian distribution has been useful in statistics. This distribution has been used in extensive applications, for example, physics, engineering, and biology. It is suited for the rightskewed data analysis. In this research, we are interested in studying the maximum likelihood equations and finding the Fisher information matrix to construct asymptotic confidence ellipse for the length-biased inverse Gaussian distribution by comparing a coverage probability with a confidence coefficient of 0.98 of confidence ellipses for cases of sample sizes n = 10, 20, 30, 50, 60, 100, 500, and 1,000 parameter λ = 1, 3, 5, 10, 15, 20 and parameter μ = 1. Monte Carlo simulations are considered with 10,000 iterations by using program R (3.4.3).
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Applied Science Research Articles
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References
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[17] C. R. Robert and G. Casella, “Monte Carlo Optimization,” in Introducing Monte Carlo Methods with R, New York : Springer, 2009, pp. 125–165.
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[21] N. Duangchana and K. Budsaba, “Asymptotic confidence ellipses of parameters for the inverse Gaussian distribution,” Thammasat International Journal of Science and Technology, vol. 19, no. 2, pp. 22–29, 2014.
[2] M. Ahsanllah and S. Kirmani, “A characterization of the wald distribution,” Naral Research Logistics Quarterly, vol. 31, pp. 155–158, 1984.
[3] R. Khattree, “Characterization of inversegaussian and gamma distributions through their length-biased distributions,” IEEE Transactions on Reliability, vol. 38, pp. 610–611, 1989.
[4] G. Patil and C. Rao, “Weighted distributions: A survey of their applications,” in Applications of statistics, Amsterdam, Netherlands: North Holland Publishing Company, 1977, pp. 383–405.
[5] G. Patil and C. Rao, “Weighted distributions and size-biased sampling with applications to wildlife Populations and Human Families,” BIOMETRICS, vol. 34, pp. 179–189, 1978.
[6] S. Blumenthal, “Proportional sampling in life length studies,” Technometrics, vol. 9, no. 2, pp. 205–218, 1967.
[7] R. L. Scheaffer, “Size-biased sampling,” Technometrics, vol. 14, no. 3, pp. 635–644, 1972.
[8] R. Simon, “Length biased sampling in etiologic studies,” American Journal of Epidemiology, vol. 111, no. 4, pp. 444–452, 1980.
[9] A. Cnaan, “Survival models with two phases and length biased sampling,” Communications in Statistics-Theory and Methods, vol. 14, no. 4, pp. 861–886, 1985.
[10] R. C. Gupta and S. Tripathi, “A comparison between the ordinary and length biased modified power series distributions with applications,” Communication s in Statistics, vol. 16, no. 4, pp. 1195–1206, 1987.
[11] P. K. Sen, “What do the arithmetic, geometric and harmonic means tell us in length-biased sampling?,” Statistics and Probability Letters, vol. 5, pp. 95–98, 1987.
[12] R. C. Gupta and S. Kirmani, “On order relations between reliability measures of two distributions,” Stochastic Models, vol. 1, no. 3, pp. 149–156, 1987.
[13] O. Akman and R. C. Gupta, “A comparison of various estimators of the mean of an inverse Gaussian distribution,” Journal of Statistical Computation and Simulation, vol. 40, no. 1–2, pp. 71–81, 1991.
[14] R. C. Gupta and O. Akman, “Statistical inference based on the length biased data for the inverse Gaussian distribution,” A Journal of Theoretical and Applied Statistics, vol. 31, no. 4, pp. 325–337, 1998.
[15] A. Ahmed and A. Abouammoh, “Characterization of gamma, inverse Gaussian, and negative binomial distributions via their length-biased distributions,” Statistical Paper, vol. 34, no. 1, pp.167–173, 1993.
[16] Y. Vardi, “Nonparametric estimation in the presence of length bias,” Annals of Statistics, vol. 10, no. 1, pp. 616–620, 1982.
[17] C. R. Robert and G. Casella, “Monte Carlo Optimization,” in Introducing Monte Carlo Methods with R, New York : Springer, 2009, pp. 125–165.
[18] B. Jorgensen, V. Seshadri, and G. A. Whitmore, “On the mixture of the inverse Gaussian distribution with its complementary reciprocal,” Scandinavian Journal of Statistics, vol. 18, no. 1, pp. 77–89, 1991.
[19] H. Cramér, Mathematical methods of statistics. Princeton, NJ, US: Princeton University Press, 1946.
[20] V. Chew, “Confidence, prediction, and tolerance regions for the multivariate normal distribution,” Journal of the American Statistical Association, vol. 61, no. 315, pp. 605–617, 1966.
[21] N. Duangchana and K. Budsaba, “Asymptotic confidence ellipses of parameters for the inverse Gaussian distribution,” Thammasat International Journal of Science and Technology, vol. 19, no. 2, pp. 22–29, 2014.
