Knowledge Network Node
China Environmental Science. Core
(Accepted Version) Online First Publishing Date: 2022-06-22 11:06:34

Correlation study of heavy metal deletion data in soil environment: Maximum likelihood method based on log-normal distributionChinese Full TextEnglish Full Text (MT)

FENG Xu;SUN Da-quan;LI Ren-ying;WANG Li-jun;HUANG Li-dong;

Abstract: The concentration of heavy metals in some samples is often at the trace level and below the detection limit of method （limit of detection/LOD）. So it is difficult to quantify the concentration of such soil sample. Data containing information below the detection limit are usually defined as the left censored data. Besides， this type of data often conforms to the log-normal distribution. so far the parameter estimation of single variable of censored data is very common. However， there are few reports on the correlation estimation of two-dimensional censorship data. Therefore， this paper is trying to estimate the correlation based on the maximum likelihood method （MLE）. A method for estimating the correlation of censored data is proposed thorough constructing the likelihood function under different scenarios. The effects of sample size， censorship ratio， population correlation coefficient and disturbance term on the accuracy of the estimated values were studied. At the same time， the accuracy of MLE was tested by comparing MLE with substitution method （usually replacing the censored part with LOD or LOD/2） and deletion method （directly delete the censored part）. The methodology was exemplified using Australian census soil data. The results show that: （1） The larger the sample size， the more accurate the MLE results in the study. When the sample size reaches 2000， the estimated value has better stability and is less affected by the censorship ratio. （2） The estimated correlation coefficient of MLE varies less with the censorship ratio （0%-90%） or the population correlation coefficient， demonstrating gradual unbiasedness and consistency. （3） The addition of disturbance terms has less impact on the accuracy of MLE， indicating that its strong robustness. （4） The accuracy of MLE is significantly better than that of deletion and substitution methods. （5） The application of actual data shows that in the Australian survey data， Ag and Hg have a high correlation， and the correlation coefficient between Hg and Hf is almost 0. This research method has good estimation performance， is helpful to realize the rational utilization of soil environmental trace substance information， and provides a feasible method for estimating the correlation coefficient of censored data in related field.
Keywords：

soil; heavy metal; censored data; bivariate log-normal distribution; maximum likelihood estimation; the correlation coefficient;

  • DOI：

    10.19674/j.cnki.issn1000-6923.20220616.001

  • Series：

    (B) Chemistry/ Metallurgy/ Environment/ Mine Industry; (A) Mathematics/ Physics/ Mechanics/ Astronomy

  • Subject：

    Environment Science and Resources Utilization; Mathematics

  • Classification Code：

    X833;O212.1

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