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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2023-03-01
|
| Series: | Austrian Journal of Statistics |
| Online Access: | https://ajs.or.at/index.php/ajs/article/view/1406 |
| _version_ | 1797849352584036352 |
|---|---|
| author | Sudeep Bapat Neeraj Joshi Ashish Shukla |
| author_facet | Sudeep Bapat Neeraj Joshi Ashish Shukla |
| author_sort | Sudeep Bapat |
| collection | DOAJ |
| description |
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.
|
| first_indexed | 2024-04-09T18:43:40Z |
| format | Article |
| id | doaj.art-21b21cf0166342f6a695523d6ebe659f |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-04-09T18:43:40Z |
| publishDate | 2023-03-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-21b21cf0166342f6a695523d6ebe659f2023-04-10T15:36:48ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2023-03-0152210.17713/ajs.v52i2.1406On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its ExtensionsSudeep Bapat0Neeraj Joshi1Ashish Shukla2Indian Institute of Management IndoreUniversity of DelhiRamanujan College, University of Delhi 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. https://ajs.or.at/index.php/ajs/article/view/1406 |
| spellingShingle | Sudeep Bapat Neeraj Joshi Ashish Shukla On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions Austrian Journal of Statistics |
| title | On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions |
| title_full | On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions |
| title_fullStr | On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions |
| title_full_unstemmed | On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions |
| title_short | On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions |
| title_sort | on fixed accuracy confidence intervals for the parameters of lindley distribution and its extensions |
| url | https://ajs.or.at/index.php/ajs/article/view/1406 |
| work_keys_str_mv | AT sudeepbapat onfixedaccuracyconfidenceintervalsfortheparametersoflindleydistributionanditsextensions AT neerajjoshi onfixedaccuracyconfidenceintervalsfortheparametersoflindleydistributionanditsextensions AT ashishshukla onfixedaccuracyconfidenceintervalsfortheparametersoflindleydistributionanditsextensions |