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Abstract
A Bayesian technique is used to approximate the tail probability of the t-distribution. A set of upper and lower bounds are obtained for this probability. Based on their simplicity and accuracy, these bounds are very adequate to use. Some members of these bounds are compared to some existing approximations. The possibility of using this new procedure for some other distributions is explored.
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References
- ABU-DAYYEH, W. and AHMED, M. 1993. Some new bounds on the tail probability of standard normal distribution. Journal of Information and Optimization Sciences 14: 155-159.
- AL-SALEH, M. FRAIWAN.1994. Mill's ratio: a Bayesian approach. Pakistan Journal of Statistics 10:629-632.
- CUCCONI, O. 1962. On simple relation between the number of degrees of freedom and the critical value of student- t. Memeorie Academia Patavina 74:179-187.
- ELFVING, G. 1955. An expansion principle for distribution functions with application to statistics. Annals Academiae Scientiarum Fennicae, series A 204:1-8.
- FISHER, R.A. 1935. The mathematical distributions used in the common tests of significance. Econometrica 3:353-365.
- GLEASON, J.R. 2000. A note on a proposed student t approximation. Computational statistics and data analysis 34:63-66.
- JOHNSON, N., KOTZ, S. and BALAKRISHNAN, N.1995. Continuous Univariate Distribution. John Wiley and sons, New York.
- LI, B. and MOOR, B. 1999. A corrected normal approximation for the student t distribution. Computational Statistics and Data Analysis 29:213-216.
- PINKHAM, R. and WILK, M. 1954. Tail areas of the t-distribution from a Mills-ratio-like expansion. Annals of Mathematical Statistics 34:335-337.
- STUART, A. and ORD, J. 1994. Kendall Advanced Theory of Statistics. Edward Arnold, London
References
ABU-DAYYEH, W. and AHMED, M. 1993. Some new bounds on the tail probability of standard normal distribution. Journal of Information and Optimization Sciences 14: 155-159.
AL-SALEH, M. FRAIWAN.1994. Mill's ratio: a Bayesian approach. Pakistan Journal of Statistics 10:629-632.
CUCCONI, O. 1962. On simple relation between the number of degrees of freedom and the critical value of student- t. Memeorie Academia Patavina 74:179-187.
ELFVING, G. 1955. An expansion principle for distribution functions with application to statistics. Annals Academiae Scientiarum Fennicae, series A 204:1-8.
FISHER, R.A. 1935. The mathematical distributions used in the common tests of significance. Econometrica 3:353-365.
GLEASON, J.R. 2000. A note on a proposed student t approximation. Computational statistics and data analysis 34:63-66.
JOHNSON, N., KOTZ, S. and BALAKRISHNAN, N.1995. Continuous Univariate Distribution. John Wiley and sons, New York.
LI, B. and MOOR, B. 1999. A corrected normal approximation for the student t distribution. Computational Statistics and Data Analysis 29:213-216.
PINKHAM, R. and WILK, M. 1954. Tail areas of the t-distribution from a Mills-ratio-like expansion. Annals of Mathematical Statistics 34:335-337.
STUART, A. and ORD, J. 1994. Kendall Advanced Theory of Statistics. Edward Arnold, London