Sequential analysis and robustness study for the parameters of positive exponential family of distributions with known coefficient of variation. (English) Zbl 1496.62138
Summary: In the present paper, we consider the positive exponential family of distributions, which has three parameters \(\theta, \nu\) and \(\rho\). On assigning different values to these parameters, it covers many distributions. For the testing of hypotheses regarding the parameters \(\theta\) and \(\nu\) a sequential testing procedures and robustness of the operating characteristics and average sample number functions are derived. The robustness of the sequential probability ratio test for the parameter \(\theta\) when the coefficient of variation is known are also obtained. The acceptance and rejection regions for the null hypotheses \(H_0\) against the alternative hypotheses \(H_1\) are also studied and presented through a graph. The numerical values of operating characteristics and average sample number function are presented in the tables and graphs.
MSC:
| 62L10 | Sequential statistical analysis |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 62N05 | Reliability and life testing |
Keywords:
PEFD; sequential probability ratio test; operating characteristics; average sample number; acceptance and rejection regions; null hypotheses; alternative hypotheses; type I error and type II errorReferences:
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