Bias Correction Method for Log-Power-Normal Distribution
The log-power-normal distribution is a generalized version of the log-normal distribution. The maximum likelihood estimation method is the most popular method to obtain the estimates of the log-power-normal distribution parameters. In this article, we investigate the performance of the maximum likel...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/6/955 |
| _version_ | 1797445395732758528 |
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| author | Tzong-Ru Tsai Yuhlong Lio Ya-Yen Fan Che-Pin Cheng |
| author_facet | Tzong-Ru Tsai Yuhlong Lio Ya-Yen Fan Che-Pin Cheng |
| author_sort | Tzong-Ru Tsai |
| collection | DOAJ |
| description | The log-power-normal distribution is a generalized version of the log-normal distribution. The maximum likelihood estimation method is the most popular method to obtain the estimates of the log-power-normal distribution parameters. In this article, we investigate the performance of the maximum likelihood estimation method for point and interval inferences. Moreover, a simple method that has less impact from the subjective selection of the initial solutions to the model parameters is proposed. The bootstrap bias correction method is used to enhance the estimation performance of the maximum likelihood estimation method. The proposed bias correction method is simple for use. Monte Carlo simulations are conducted to check the quality of the proposed bias correction method. The simulation results indicate that the proposed bias correction method can improve the performance of the maximum likelihood estimation method with a smaller bias and provide a coverage probability close to the nominal confidence coefficient. Two real examples about the air pollution and cement’s concrete strength are used for illustration. |
| first_indexed | 2024-03-09T13:25:14Z |
| format | Article |
| id | doaj.art-4fb6cfed8c544cbfa54e0de3950cf855 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:25:14Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4fb6cfed8c544cbfa54e0de3950cf8552023-11-30T21:24:37ZengMDPI AGMathematics2227-73902022-03-0110695510.3390/math10060955Bias Correction Method for Log-Power-Normal DistributionTzong-Ru Tsai0Yuhlong Lio1Ya-Yen Fan2Che-Pin Cheng3Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanDepartment of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USADepartment of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanDepartment of Information Management, Tamkang University, Tamsui District, New Taipei City 251301, TaiwanThe log-power-normal distribution is a generalized version of the log-normal distribution. The maximum likelihood estimation method is the most popular method to obtain the estimates of the log-power-normal distribution parameters. In this article, we investigate the performance of the maximum likelihood estimation method for point and interval inferences. Moreover, a simple method that has less impact from the subjective selection of the initial solutions to the model parameters is proposed. The bootstrap bias correction method is used to enhance the estimation performance of the maximum likelihood estimation method. The proposed bias correction method is simple for use. Monte Carlo simulations are conducted to check the quality of the proposed bias correction method. The simulation results indicate that the proposed bias correction method can improve the performance of the maximum likelihood estimation method with a smaller bias and provide a coverage probability close to the nominal confidence coefficient. Two real examples about the air pollution and cement’s concrete strength are used for illustration.https://www.mdpi.com/2227-7390/10/6/955bias correctionlog-power-normal distributionmaximum likelihood estimationMonte Carlo simulationquality control |
| spellingShingle | Tzong-Ru Tsai Yuhlong Lio Ya-Yen Fan Che-Pin Cheng Bias Correction Method for Log-Power-Normal Distribution Mathematics bias correction log-power-normal distribution maximum likelihood estimation Monte Carlo simulation quality control |
| title | Bias Correction Method for Log-Power-Normal Distribution |
| title_full | Bias Correction Method for Log-Power-Normal Distribution |
| title_fullStr | Bias Correction Method for Log-Power-Normal Distribution |
| title_full_unstemmed | Bias Correction Method for Log-Power-Normal Distribution |
| title_short | Bias Correction Method for Log-Power-Normal Distribution |
| title_sort | bias correction method for log power normal distribution |
| topic | bias correction log-power-normal distribution maximum likelihood estimation Monte Carlo simulation quality control |
| url | https://www.mdpi.com/2227-7390/10/6/955 |
| work_keys_str_mv | AT tzongrutsai biascorrectionmethodforlogpowernormaldistribution AT yuhlonglio biascorrectionmethodforlogpowernormaldistribution AT yayenfan biascorrectionmethodforlogpowernormaldistribution AT chepincheng biascorrectionmethodforlogpowernormaldistribution |