Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters
As a result of asymmetry in practical problems, the Lognormal distribution is more suitable for data modeling in biological and economic fields than the normal distribution, while biases of maximum likelihood estimators are regular of the order <inline-formula> <math display="inline&qu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/6/968 |
| _version_ | 1797565986576007168 |
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| author | Shuyi Wang Wenhao Gui |
| author_facet | Shuyi Wang Wenhao Gui |
| author_sort | Shuyi Wang |
| collection | DOAJ |
| description | As a result of asymmetry in practical problems, the Lognormal distribution is more suitable for data modeling in biological and economic fields than the normal distribution, while biases of maximum likelihood estimators are regular of the order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>n</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, especially in small samples. It is of necessity to derive logical expressions for the biases of the first-order and nearly consistent estimators by bias correction techniques. Two methods are adopted in this article. One is the Cox-Snell method. The other is the resampling method known as parametric Bootstrap. They can improve maximum likelihood estimators performance and correct biases of the Lognormal distribution parameters. Through Monte Carlo simulations, we obtain average root mean squared error and bias, which are two important indexes to compare the effect of different methods. The numerical results reveal that for small and medium-sized samples, the performance of analytical bias correction estimation is superior than bootstrap estimation and classical maximum likelihood estimation. Finally, an example is given based on the actual data. |
| first_indexed | 2024-03-10T19:20:26Z |
| format | Article |
| id | doaj.art-f77eff42e9134d408f699cb70d8df396 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T19:20:26Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f77eff42e9134d408f699cb70d8df3962023-11-20T03:03:03ZengMDPI AGSymmetry2073-89942020-06-0112696810.3390/sym12060968Corrected Maximum Likelihood Estimations of the Lognormal Distribution ParametersShuyi Wang0Wenhao Gui1Department of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaDepartment of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaAs a result of asymmetry in practical problems, the Lognormal distribution is more suitable for data modeling in biological and economic fields than the normal distribution, while biases of maximum likelihood estimators are regular of the order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>n</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, especially in small samples. It is of necessity to derive logical expressions for the biases of the first-order and nearly consistent estimators by bias correction techniques. Two methods are adopted in this article. One is the Cox-Snell method. The other is the resampling method known as parametric Bootstrap. They can improve maximum likelihood estimators performance and correct biases of the Lognormal distribution parameters. Through Monte Carlo simulations, we obtain average root mean squared error and bias, which are two important indexes to compare the effect of different methods. The numerical results reveal that for small and medium-sized samples, the performance of analytical bias correction estimation is superior than bootstrap estimation and classical maximum likelihood estimation. Finally, an example is given based on the actual data.https://www.mdpi.com/2073-8994/12/6/968asymmetry of lognormal distributionmaximum likelihoodparametric bootstrap resampling methodCox-Snell bias-corrected methodMonte Carlo simulation |
| spellingShingle | Shuyi Wang Wenhao Gui Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters Symmetry asymmetry of lognormal distribution maximum likelihood parametric bootstrap resampling method Cox-Snell bias-corrected method Monte Carlo simulation |
| title | Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters |
| title_full | Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters |
| title_fullStr | Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters |
| title_full_unstemmed | Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters |
| title_short | Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters |
| title_sort | corrected maximum likelihood estimations of the lognormal distribution parameters |
| topic | asymmetry of lognormal distribution maximum likelihood parametric bootstrap resampling method Cox-Snell bias-corrected method Monte Carlo simulation |
| url | https://www.mdpi.com/2073-8994/12/6/968 |
| work_keys_str_mv | AT shuyiwang correctedmaximumlikelihoodestimationsofthelognormaldistributionparameters AT wenhaogui correctedmaximumlikelihoodestimationsofthelognormaldistributionparameters |