Statistical Inference for k (k>=3) Lognormal Means from Left Censored Data
Keywords:multiple detection limits; left censored data; normal and lognormal distributions; maximum likelihood estimators; expectation maximization algorithm; likelihood ratio test
The occurrence of censored data due to less than detectable measurements is a common problem with environmental data such as quality and quantity monitoring applications of water, soil, and air samples. The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. Over the past decades, various methods for comparing the parameters of two lognormal distributions in the presence censored data have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. As a model distribution of measured environmental and/or biomedical data, log-normal distribution is considered. Logmormal means can be compared either by confidence intervals or hypothesis testing procedures. In this article, a new test procedure for comparing the means of k (k >= 3) lognormal distributions in the presence of left-censored data is introduced and evaluated. Asymptotic chi-square test is used in the proposed test procedure. A simulation study was performed to examine the power and the size of the proposed test procedure introduced in this article utilizing a computer program written in the R language. We find analytically that the considered test procedure is doing well through comparing the size and power of the statistic test.
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