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Various properties of the mixed exponential hazard rate and reliability are discussed. Particular attention is given to the relationship between the mixed hazard rate h(t) and the mixing density g(λ). Characteristic functions are derived and expressions relating integral transforms (Laplace, Fourier and Mellin) to the mixed exponential family are presented. A complex contour integration is used to invert a given mixed R(t) and recover the mixing density g(λ). Several generalized mixed reliability functions and the corresponding mixing densities are provided together with their Muth global classification measures. The relationship of the mixed exponential hazard rate to the intensity function of some generalized stochastic point processes is discussed. Results for a mixed Weibull density are also included.
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McNolty et al. (1980) studied this question.
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