In this paper, we study a general structure for the so-called Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions. Through examples we show how to use the proposed structure to study dependence properties of the FGM type distributions by a general approach.
We derive some new results for preservation of various stochastic orders and aging classes under weighted distributions. The corresponding reversed preservation properties as straightforward conclusions of the obtained results for the direct preservation properties, are developed. Damage model of Rao, residual lifetime distribution, proportional hazards and proportional reversed hazards models are discussed as special weighted distributions to try some of our results.
Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via -function defined by Cacoullos and Papathanasiou...
In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences...
Some maximal inequalities for quadratic forms of independent and linearly negative quadrant dependent fuzzy random variables are established. Strong convergence of such quadratic forms are proved based on the martingale theory. A weak law of large numbers for linearly negative quadrant dependent fuzzy random variables is stated and proved.
Although the total time on test () transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the transform for the weighted random variables and investigates the behavior...
In this paper, we obtain lower bounds for the variance of a function of random variables in terms of measures of reliability and entropy. Also based on the obtained characterization via the lower bounds for the variance of a function of random variable , we find a characterization of the weighted function corresponding to density function , in terms of Chernoff-type inequalities. Subsequently, we obtain monotonic relationships between variance residual life and dynamic cumulative residual entropy...
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