Mohamed Kayid

Recently, the uncertainty aspects of record values have been increasingly studied in the literature. In this paper, we study the residual Tsallis entropy of upper record values coming from random samples. In the continuous case, we define the Tsallis entropy quantity for the residual lifetime of upper record values in general distributions as the residual Tsallis entropy of upper record values coming from a uniform distribution. We also obtain a lower bound on the residual Tsallis entropy of upper data set values originating from an arbitrary continuous probability distribution. We also discuss the monotonic property of the residual Tsallis entropy of upper data sets.

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve the fit. In this study, we investigated a further extension of the quasi-Lindley model. This extension was asymmetrically distributed on the positive real number line. Maximum likelihood, least square error, Anderson–Darling, and expectation maximization algorithms were used to estimate the parameters studied. All techniques provided accurate and reliable estimates of the parameters. However, the mean square error of the expectation-maximization approach was lower. The usefulness of the proposed model was demonstrated by analyzing a reliability data set, and the analysis showed that it outperformed all other alternative models.

In this paper, a novel strategy is employed in which a degradation model affects the implied distribution of lifetimes differently compared to the traditional method. It is recognized that an existing link between the degradation measurements and failure time constructs the underlying time-to-failure model. We assume in this paper that the conditional survival function of a device under degradation is a piecewise linear function for a given level of degradation. The multiplicative degradation model is used as the underlying degradation model, which is often the case in many practical situations. It is found that the implied lifetime distribution is a classical mixture model. In this mixture model, the time to failure lies with some probabilities between two first passage times of the degradation process to reach two specified values. Stochastic comparisons in the model are investigated when the probabilities are changed. To illustrate the applicability of the results, several examples are given in cases when typical degradation models are candidates.