Prediction of future failures in the log-logistic distribution based on hybrid censored data

We consider the prediction of future observations from the log-logistic distribution. The data is assumed hybrid right censored with possible left censoring. Different point predictors were derived. Specifically, we obtained the best unbiased, the conditional median, and the maximum likelihood predictors. Prediction intervals were derived using suitable pivotal quantities and intervals based on the highest density. We conducted a simulation study to compare the point and interval predictors. It is found that the point predictor BUP and the prediction interval HDI have the best overall performance. An illustrative example based on real data is given.

Simulation of inference test performance for minimum inhibitory concentration censored data

The estimation of the minimum inhibitory concentration is usually performed by a method of serial dilutions by a factor of 2, introducing the overestimation of antimicrobial efficacy, quantified by a simulation model that shows that the variability of the bias is higher for the standard deviation, being dependent on the metric distance to the values of the concentrations used. We use a methodological approach through modeling and simulation for the measurement error of physical variables with censored information, proposing a new inference method based on the calculation of the exact probability for the set of possible samples from nmeasurements that allows quantifying the p-value in one or two independent sample tests for the comparison of censored data means. Tests based on exact probability methods offer a reasonable solution for small sample sizes, with statistical power varying according to the hypothesis evaluated, providing insight into the limitations of censored data analysis and providing a tool for decision making in the diagnosis of antimicrobial efficacy.

Inferences for Exponentiated Gamma Constant-Stress Partially Accelerated Life Test Model Based on Generalized Type-I Hybrid Censored Data

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods.

Microbial-Maximum Likelihood Estimation Tool for Microbial Quantification in Food From Left-Censored Data Using Maximum Likelihood Estimation for Microbial Risk Assessment

In food microbial measurements, when most or very often bacterial counts are below to the limit of quantification (LOQ) or the limit of detection (LOD) in collected food samples, they are either ignored or a specified value is substituted. The consequence of this approach is that it may lead to the over or underestimation of quantitative results. A maximum likelihood estimation (MLE) or Bayesian models can be applied to deal with this kind of censored data. Recently, in food microbiology, an MLE that deals with censored results by fitting a parametric distribution has been introduced. However, the MLE approach has limited practical application in food microbiology as practical tools for implementing MLE statistical methods are limited. We therefore developed a user-friendly MLE tool (called “Microbial-MLE Tool”), which can be easily used without requiring complex mathematical knowledge of MLE but the tool is designated to adjust log-normal distributions to observed counts, and illustrated how this method may be implemented for food microbial censored data using an Excel spreadsheet. In addition, we used two case studies based on food microbial laboratory measurements to illustrate the use of the tool. We believe that the Microbial-MLE tool provides an accessible and comprehensible means for performing MLE in food microbiology and it will also be of help to improve the outcome of quantitative microbial risk assessment (MRA).