Fixed width confidence interval for the parameter of U (aθ, bθ) distribution ∗

V N  Kadam; H S Patil

doi:10.48165/

Authors

V N Kadam Department of Statistics, S. B. Zadbuke Mahavidyalaya, Barsi, Maharashtra – 413401, India.
H S Patil Department of Statistics, S. B. Zadbuke Mahavidyalaya, Barsi, Maharashtra – 413401, India.

DOI:

https://doi.org/10.48165/

Keywords:

Non–coverage probability, sequential procedure, numerical evaluation

Abstract

In the literature, an extensive work on sequential fixed width confidence intervals for the parameter θ of the U (0, θ) distribution is available. In this article, we propose a sequential fixed width (1 − α) level confidence interval for θ of U (aθ, bθ) distri bution, where 0 < a < b are increasing and known. Further we obtain the average sample number (ASN) function of the proposed procedure.

References

Akahira, M. and Koike, K. (2005). Sequential interval estimation of allocation parameter with the fixed width in the uniform distribution with an unknown scale parameter, Sequential Analysis, 24, 63–75.

Cooke, P.J. (1971). Sequential estimation in the uniform density, Journal of American Statistical Association, 66(335), 614– 617.

Cooke, P.J. (1973). Two-stage sequential estimation in uniform density, Journal of American Statistical Association 68(341), 107–108.

Govindarajulu, Z. (1997). A note on two-stage and sequential fixed-width intervals for the param eter in the uniform density, Statistical Probability Letters, 36, 179–188.

Govindarajulu, Z.(1999). Erratum: a note on two-stage and sequential fixed-width intervals for the parameter in the uniform density, Statistical Probability Letters, 42, 213–215. [6] Graybill, A. and Connell, T. L.(1964). Sample size required to estimate the parameter in uniform density within ‘d’ units of true value, Journal of American Statistical Association, 59, 550–556. [7] Koike, K.(2007). Sequential interval estimation of a location parameter with fixed width in the non-regular case, Sequential Analysis, 26, 63–70.

Patil, H.S. (2012). Two-stage estimation procedure for the parameter of distribution, Calcutta Statistical Association Bulletin, 64, 257–264.

Patil, H.S. (2014). A purely sequential estimation procedure for the parameter of distribution, Calcutta Statistical Association Bulletin, 66, 235–240.

Patil, H.S., and Rattihalli, R.N. (2007-2008). Sequential fixed width confidence interval for the parameter when limits depend upon the parameter, Gujarat Statistical Review, 34 & 35, 45–55. [11] Patil, H.S., and Rattihalli, R.N. (2011). Fixed width confidence interval for distribution, Commu nication in Statistics (Theory and Methods), 40, 907-915.

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