In this note we investigate proximity between exponential and IFR (increasing failure rate) distributions. The result is: if F[epsilon]IFR with the first and second moment [mu] and [mu]2, respectively, then supt[greater-or-equal, slanted]0(t)-exp(-t/[mu])[less-than-or-equals, slant](1-ex where...

A characterization, extending a recent result due to Kotz and Steutel, is presented for exponential distributions. Links are made with other clearly related results, and multivariate analogues are considered.

In this note we investigate proximity between exponential and DMRL (decreasing mean residual life) distributions. The result is: If F [epsilon] DMRL with the first and second moment [mu] and [mu]2, respectively, then , where [varrho] = 1 - [mu]2/(2[mu]2), and the bound is sharp.

A simple time series model for bivariate exponential variables having first-order autoregressive structure is presented, the BEAR(1) model. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR(2)). The process is Markovian in...

A continuous c.d.f. F(x), strictly increasing for x 0, is exponential if and only if Xj, n - Xi, n and Xj-i, n-i have identical distribution for some i, n, J = j1, j2, 1 [less-than-or-equals, slant] i j1 j2 [less-than-or-equals, slant] n, n [greater-or-equal, slanted] 3. A new proof of this...