As a result of the adaptability in fitting time-to-failure of a very widespread multiplicity to multifaceted mechanisms, the Weibull distribution has assumed the centre stage especially in the field of life-testing and reliability/survival analysis. It has shown to be very useful for modeling and analyzing life time data in medical, biological and engineering sciences, Lawless [17]. Much of the attractiveness of the Weibull distribution is due to the wide variety of shapes it can assume by altering its parameters. According to [19], "A data sample is said to be censored when, either by accident or design, the value of the variables under investigation is unobserved for some of the items in the sample." Maximum Likelihood Estimator (MLE) is quiet efficient and very popular both in literature and practice. Bayesian approach has been employed for estimating parameters. Some researchers have made comparisons of MLE and that of the Bayesian approach in estimating the survival function and the parameters of the Weibull distribution. According to [20] determined the Bayes estimates of the reliability function and the hazard rate of the Weibull failure time distribution by employing squared error loss function, [1] studied the approximate Bayesian estimates for the Weibull reliability function and hazard rate from censored data by employing a new method that has the potential of reducing the number of terms in Lindley procedure, and [5] conducted a study on Bayesian survival estimator for Weibull distribution with censored data using squared error loss function with Jeffreys prior amongst others.[10] applied Bayesian estimation, for the two-parameter Weibull distribution using extension of Jeffreys" prior information with three loss functions, [21] considered Bayesian estimation and prediction for Weibull model with progressive censoring. Other recent papers employing different
We have obtained some results on oscillatory behavior of third order nonlinear neutral difference equations of the form Δ 3 ( y m 1 + b y m 1 − δ 1 − c y m 1 + δ 2 ) β = q m 1 − 1 y m 1 − ρ 1 − 1 γ − q m 1 y m 1 − ρ 1 γ + p m 1 − 1 y m 1 + ρ 2 − 1 y − p m 1 y m 1 + ρ 2 γ Δ 3 ( y m 1 + b y m 1 − δ 1 − c y m 1 + δ 2 ) β = q m 1 − 1 y m 1 − ρ 1 − 1 γ − q m 1 y m 1 − ρ 1 γ + p m 1 − 1 y m 1 + ρ 2 − 1 y − p m 1 y m 1 + ρ 2 γ where β and γ are odd integers with γ ≥ 1. Example is provided to illustrate the results.
A Receiver Operating Characteristic (ROC) curve provides quick access to the quality of classification in many medical diagnoses. The Weibull distribution has been observed as one of the most useful distributions, for modeling and analyzing lifetime data in Engineering, Biology, Survival and other fields. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. In this paper, we examine the performance of Bayesian Estimator using Jeffreys‘ Prior Information and Extension of Jeffreys‘ Prior Information with three Loss functions, namely, the Linear Exponential Loss,General Entropy Loss, and Square Error Loss for estimating the AUC values for Constant Shape Bi-Weibull failure time distribution. Theoretical results are validated by simulation studies. Simulations indicated that estimate of AUC values were good even for relatively small sample sizes (n=25). When AUC≤0.6, which indicated a marked overlap between the outcomes in diseased and non-diseased populations. An illustrative example is also provided to explain the concepts.
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