The failure rate for the convolution of two distributions, one of which has bounded support

George Tzavelas and Konstadinos Politis

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 13, 4717-4729

Abstract: We study the behavior of the failure rate associated with the distribution of a random variable of the form X=Y+U, where Y, U are independent and U has bounded support. First, we obtain monotonicity results and bounds for the failure rate of X in the case where U has a uniform distribution and, in particular we show that, asymptotically, the failure rates of X and Y tend to the same limit. Some of the results are generalized for the case where the distribution of U is not uniform, but has bounded support. Further, we show that if the failure rate of a non negative variable X is constant in some interval (L,∞), then X can be written as the sum of two independent random variables, one of which is exponential and the other (which is not necessarily uniform) has support [0,L].

Date: 2024
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DOI: 10.1080/03610926.2023.2186729

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