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Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and is quite popular in statistical distribution theory. Entropy methods available in the literature quantify the information of a random variable with exact numbers and lacks in dealing with the interval value data. An indeterminate state of an experiment generally generates the data in interval form. The indeterminacy property of interval-valued data makes it a neutrosophic form data. This research proposed some modified forms of entropy measures for an important lifetime distribution called Weibull distribution by considering the neutrosophic form of the data. The performance of the proposed methods is assessed via a simulation study and three real-life data applications. The simulation and real-life data examples suggested that the proposed methodologies of entropies for the Weibull distribution are more suitable when the random variable of the distribution is in an interval form and has indeterminacy or vagueness in it. [ABSTRACT FROM AUTHOR]

BACKGROUND: Sputum smear microscopy is the most useful tool used for the screening of presumptive tuberculosis cases. Conventionally Ziehl-Neelsen (ZN) based staining is used to microscopically screen sputum from the presumptive Tuberculosis Cases. However, Fluorescent microscopy (FM) is now gradually replacing the conventional ZN microscopy because of its higher efficiency and efficacy in detecting Mycobacterium tuberculosis. In patients, who do not produce sufficiently high number of bacilli, and are known as Smear-negative, efficacy of both types of microscopy remains questionable as no Mycobacteria are detected in the sputum of these patients and they are falsely labelled as smear-negative. OBJECTIVE: This retrospective study was conducted on the patient samples received from different parts of Sindh to study the proportions of false-negative tuberculosis using fluorescent microscopy. MATERIALS AND METHODS: A retrospective cross-sectional study was conducted from June 2014 to June 2016 at the Tuberculosis Laboratories of Dow University of Health Sciences. Data analyzed for 1439 samples received during 24-month period, which had subsequently been confirmed by culture. All laboratory work was performed as per guidelines of the National Program. Statistical analysis was performed on MedCalc® and Open Epi®. RESULTS: During 24-month period, among the 1439 cases, 832(57.81%) were from males and 499 (34.67%) were smear negative. Culture showed that 72 (14.42%) were false-negative among all-negatives. Overall sensitivity observed was 92.21% [95%CI 90.29%-93.85%] and specificity 82.91% [95%CI 79.38%-86.06%]. The proportion of false negativity among all negatives in females (16.11%) was significantly higher (p=0.002) as compared to males (13.47%). Conclusions: Even with the introduction of Fluorescent Microscopy, smear microscopy cannot be solely relied upon for the diagnosis of tuberculosis, as considerable number of patients producing insufficient number of bacilli to be detected by microscopy. [ABSTRACT FROM AUTHOR]