Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached
Three methods of approximating the sum of lognormal variates to a lognormal distribution were studied. They were the Wilkinson approximation, the Monte Carlo version of the Wilkinson approximation and the approximation using estimated maximum likelihood lognormal parameters. The lognormal variates w...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2023
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| Online Access: | http://journalarticle.ukm.my/21554/ http://journalarticle.ukm.my/21554/1/S%2024.pdf |
| _version_ | 1848815380429012992 |
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| author | Abdul Rahman Othman, Lai, Choo Heng Aissa, Sonia Nora Muda, |
| author_facet | Abdul Rahman Othman, Lai, Choo Heng Aissa, Sonia Nora Muda, |
| author_sort | Abdul Rahman Othman, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | Three methods of approximating the sum of lognormal variates to a lognormal distribution were studied. They were the Wilkinson approximation, the Monte Carlo version of the Wilkinson approximation and the approximation using estimated maximum likelihood lognormal parameters. The lognormal variates were generated empirically using Monte Carlo simulation based on several conditions such as number of lognormal variates in the sum, number of sample points in the variates, the variates are independent and identically distributed (IID) and also not identically distributed (NIID) with lognormal parameters. Evaluation of all three lognormal approximation methods was performed using the Anderson Darling test. Results show that the approximation using estimated maximum likelihood lognormal parameters produced Type I errors close to the 0.05 target and is considered the best approximation. |
| first_indexed | 2025-11-15T00:49:04Z |
| format | Article |
| id | oai:generic.eprints.org:21554 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:49:04Z |
| publishDate | 2023 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:215542023-05-09T06:46:49Z http://journalarticle.ukm.my/21554/ Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached Abdul Rahman Othman, Lai, Choo Heng Aissa, Sonia Nora Muda, Three methods of approximating the sum of lognormal variates to a lognormal distribution were studied. They were the Wilkinson approximation, the Monte Carlo version of the Wilkinson approximation and the approximation using estimated maximum likelihood lognormal parameters. The lognormal variates were generated empirically using Monte Carlo simulation based on several conditions such as number of lognormal variates in the sum, number of sample points in the variates, the variates are independent and identically distributed (IID) and also not identically distributed (NIID) with lognormal parameters. Evaluation of all three lognormal approximation methods was performed using the Anderson Darling test. Results show that the approximation using estimated maximum likelihood lognormal parameters produced Type I errors close to the 0.05 target and is considered the best approximation. Penerbit Universiti Kebangsaan Malaysia 2023 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/21554/1/S%2024.pdf Abdul Rahman Othman, and Lai, Choo Heng and Aissa, Sonia and Nora Muda, (2023) Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached. Sains Malaysiana, 52 (1). pp. 295-304. ISSN 0126-6039 http://www.ukm.my/jsm/index.html |
| spellingShingle | Abdul Rahman Othman, Lai, Choo Heng Aissa, Sonia Nora Muda, Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| title | Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| title_full | Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| title_fullStr | Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| title_full_unstemmed | Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| title_short | Approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| title_sort | approximation of the sum of independent lognormal variates using lognormal distribution by maximum likelihood estimation approached |
| url | http://journalarticle.ukm.my/21554/ http://journalarticle.ukm.my/21554/ http://journalarticle.ukm.my/21554/1/S%2024.pdf |