Research Article An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health Navid Feroze , 1 Ali Akgul, 2 Taghreed M. Jawa , 3 Neveen Sayed-Ahmed, 3 and Rashid Ali 4 1 Department of Statistics, The University of Azad Jammu and Kashmir, Muzaffarabad, Pakistan 2 Department of Mathematics, Siirt University, Art and Science Faculty, 56100 Siirt, Turkey 3 Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia 4 School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China Correspondence should be addressed to Navid Feroze; navidferoz@gmail.com Received 28 April 2022; Accepted 7 June 2022; Published 12 July 2022 Academic Editor: Sania Qureshi Copyright © 2022 Navid Feroze et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Analysis of environmental data with lower detection limits (LDL) using mixture models has recently gained importance. However, only a particular type of mixture models under classical estimation methods have been used in the literature. We have proposed the Bayesian analysis for the said data using mixture models. In addition, an optimal mixture distribution to model such data has been explored. The sensitivity of the proposed estimators with respect to LDL, model parameters, hyperparameters, mixing weights, loss functions, sample size, and Bayesian estimation methods has also been proposed. The optimal number of components for the mixture has also been explored. As a practical example, we analyzed two environmental datasets involving LDL. We also compared the proposed estimators with existing estimators, based on different goodness of fit criteria. The results under the proposed estimators were more convincing as compared to those using existing estimators. 1. Introduction The environmental studies often encounter the exposure measurements falling below the LDL. These nondetectable observations are considered left censored observations [1, 2]. Hughes [3] discussed that the difficulty in modeling the environmental concentration datasets arises when some of the measurements are below the LDL. As the proportion of censored observations may not be trivial, failure to adjust the censoring in the analysis can produce seriously biased results with inflated variances. The most convenient method to adjust the censoring is to replace the censored observation by the detection limit. However, statistical properties of such methods are obscured. As an improvement, Paxton et al. [4] proposed the iterative imputation technique to settle the censoring issue, but this method did not consider the corre- lated structure of the data and parametric estimates. Some authors have proposed the standard statistical dis- tributions to model the left censored datasets. For example, Mitra and Kundu [5] used generalized exponential distribu- tion, Bhaumik et al. [6] employed normal distribution, Leith et al. [7] and Jin et al. [8] used log-normal distribution, and Asgharzadeh et al. [9] considered Weibull model to model the left censored data from different situations. However, varying modeling capabilities of these models to model the left censored data has been reported by Vizard et al. [10]. Further, Moulton and Halsey [11] raised several concerns over using a standard statistical model to deal with such data. They argued that these datasets may be highly skewed to make most of the standard models inappropriate for anal- ysis. Further, there may exist an additional subpopulation of the observations falling below the detection limit making the data heterogeneous or multimodal. Following these argu- ments, Moulton and Halsey [11] suggested the use of gamma mixture model (in their case) to model the left cen- sored HIV RNA dataset. Taylor et al. [12] also emphasized that in case of larger proportion of nondetectable observa- tions, a suitable model for analysis should be explored. They Hindawi Computational and Mathematical Methods in Medicine Volume 2022, Article ID 4414582, 15 pages https://doi.org/10.1155/2022/4414582