Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications
The notion of length-biased distribution can be used to develop adequate models. Length-biased distribution was known as a special case of weighted distribution. In this work, a new class of length-biased distribution, namely the two-sided length-biased inverse Gaussian distribution (TS-LBIG), was i...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/10/1965 |
| _version_ | 1797469879237869568 |
|---|---|
| author | Teerawat Simmachan Wikanda Phaphan |
| author_facet | Teerawat Simmachan Wikanda Phaphan |
| author_sort | Teerawat Simmachan |
| collection | DOAJ |
| description | The notion of length-biased distribution can be used to develop adequate models. Length-biased distribution was known as a special case of weighted distribution. In this work, a new class of length-biased distribution, namely the two-sided length-biased inverse Gaussian distribution (TS-LBIG), was introduced. The physical phenomenon of this scenario was described in a case of cracks developing from two sides. Since the probability density function of the original TS-LBIG distribution cannot be written in a closed-form expression, its generalization form was further introduced. Important properties such as the moment-generating function and survival function cannot be provided. We offered a different approach to solving this problem. Some distributional properties were investigated. The parameters were estimated by the method of the moment. Monte Carlo simulation studies were carried out to appraise the performance of the suggested estimators using bias, variance, and mean square error. An application of a real dataset was presented for illustration. The results showed that the suggested estimators performed better than the original study. The proposed distribution provided a more appropriate model than other candidate distributions for fitting based on Akaike information criterion. |
| first_indexed | 2024-03-09T19:27:18Z |
| format | Article |
| id | doaj.art-e6fd9b35f2044da198edd2e099f418c2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T19:27:18Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e6fd9b35f2044da198edd2e099f418c22023-11-24T02:49:46ZengMDPI AGSymmetry2073-89942022-09-011410196510.3390/sym14101965Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and ApplicationsTeerawat Simmachan0Wikanda Phaphan1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 10120, ThailandDepartment of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandThe notion of length-biased distribution can be used to develop adequate models. Length-biased distribution was known as a special case of weighted distribution. In this work, a new class of length-biased distribution, namely the two-sided length-biased inverse Gaussian distribution (TS-LBIG), was introduced. The physical phenomenon of this scenario was described in a case of cracks developing from two sides. Since the probability density function of the original TS-LBIG distribution cannot be written in a closed-form expression, its generalization form was further introduced. Important properties such as the moment-generating function and survival function cannot be provided. We offered a different approach to solving this problem. Some distributional properties were investigated. The parameters were estimated by the method of the moment. Monte Carlo simulation studies were carried out to appraise the performance of the suggested estimators using bias, variance, and mean square error. An application of a real dataset was presented for illustration. The results showed that the suggested estimators performed better than the original study. The proposed distribution provided a more appropriate model than other candidate distributions for fitting based on Akaike information criterion.https://www.mdpi.com/2073-8994/14/10/1965method of momentlifetime distributionparametrizationre-parameterized distributionlength-biased distribution |
| spellingShingle | Teerawat Simmachan Wikanda Phaphan Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications Symmetry method of moment lifetime distribution parametrization re-parameterized distribution length-biased distribution |
| title | Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications |
| title_full | Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications |
| title_fullStr | Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications |
| title_full_unstemmed | Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications |
| title_short | Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications |
| title_sort | generalization of two sided length biased inverse gaussian distributions and applications |
| topic | method of moment lifetime distribution parametrization re-parameterized distribution length-biased distribution |
| url | https://www.mdpi.com/2073-8994/14/10/1965 |
| work_keys_str_mv | AT teerawatsimmachan generalizationoftwosidedlengthbiasedinversegaussiandistributionsandapplications AT wikandaphaphan generalizationoftwosidedlengthbiasedinversegaussiandistributionsandapplications |