On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions
The purpose of the present paper is to deal with sequential estimation of the parameter θ in a Lindley distribution. A fixed-accuracy confidence interval for θ with a preassigned confidence coefficient is developed. It is established that, no fixed sample size procedure can solve the estimation pro...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2023-03-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://ajs.or.at/index.php/ajs/article/view/1406 |
| Summary: | The purpose of the present paper is to deal with sequential estimation of the parameter θ in a Lindley distribution. A fixed-accuracy confidence interval for θ with a preassigned confidence coefficient is developed. It is established that, no fixed sample size procedure can solve the estimation problem and hence a purely sequential methodology is proposed to deal with the situation. The first-order asymptotic efficiency and consistency properties associated with our purely sequential strategy are derived. Similar estimation strategies are also outlined for a few other extensions of the Lindley distribution. Extensive simulation analysis is carried out to validate the theoretical findings. We also provide a real data example, where we estimate the parameter related to the “initial mass function" for a particular cluster of stars.
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| ISSN: | 1026-597X |