On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions
ABSTRACT
The main aim of the present paper is to study the robustness of the developed sequential probability ratio test (SPRT) for testing the hypothesis about scale parameter of gamma distribution with known shape parameter and exponential distribution with location parameter. The robustness of the SPRT for scale parameter of gamma distribution is studied when the shape parameter has undergone a change. The similar study is conducted for the scale parameter of exponential distribution when the location parameter has undergone a change. The expressions for operating characteristic and average sample number functions are derived. It is found in both the cases that the SPRT is robust only when there is a slight variation in the shape and location parameter in the respective distributions.
The main aim of the present paper is to study the robustness of the developed sequential probability ratio test (SPRT) for testing the hypothesis about scale parameter of gamma distribution with known shape parameter and exponential distribution with location parameter. The robustness of the SPRT for scale parameter of gamma distribution is studied when the shape parameter has undergone a change. The similar study is conducted for the scale parameter of exponential distribution when the location parameter has undergone a change. The expressions for operating characteristic and average sample number functions are derived. It is found in both the cases that the SPRT is robust only when there is a slight variation in the shape and location parameter in the respective distributions.
KEYWORDS
Gamma Distribution, Sequential Probability Ratio Test, Operating Characteristic Function, Average Sample Number Function, Robustness
Gamma Distribution, Sequential Probability Ratio Test, Operating Characteristic Function, Average Sample Number Function, Robustness
Cite this paper
P. Pandit and N. Gudaganavar, "On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions," Applied Mathematics, Vol. 1 No. 4, 2010, pp. 274-278. doi: 10.4236/am.2010.14034.
P. Pandit and N. Gudaganavar, "On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions," Applied Mathematics, Vol. 1 No. 4, 2010, pp. 274-278. doi: 10.4236/am.2010.14034.
References
[1] R. E. Barlow and E. Proschan, “Exponential Life Test Procedures When the Distribution under Test has Monotone Failure Rate,” Journal of American Statistic Association, Vol. 62, No. 318, 1967, pp. 548-560. [2] L. Harter and A. H. Moore, “An Evaluation of Exponential and Weibull Test Plans,” IEEE Transactions on Reliability, Vol. 25, No. 2, 1976, pp. 100-104. [3] E. R. Montagne and N. D. Singpurwalla, “Robustness of Sequential Exponential Life-Testing Procedures,” Journal of American Statistic Association, Vol. 80, No. 391, 1985, pp. 715-719. [4] A. Wald, “Sequential Analysis,” John Wiley, New York, 1947.
[1] R. E. Barlow and E. Proschan, “Exponential Life Test Procedures When the Distribution under Test has Monotone Failure Rate,” Journal of American Statistic Association, Vol. 62, No. 318, 1967, pp. 548-560. [2] L. Harter and A. H. Moore, “An Evaluation of Exponential and Weibull Test Plans,” IEEE Transactions on Reliability, Vol. 25, No. 2, 1976, pp. 100-104. [3] E. R. Montagne and N. D. Singpurwalla, “Robustness of Sequential Exponential Life-Testing Procedures,” Journal of American Statistic Association, Vol. 80, No. 391, 1985, pp. 715-719. [4] A. Wald, “Sequential Analysis,” John Wiley, New York, 1947.