DETERMINATION OF CHANGE POINTS OF NON-MONOTONIC FAILURE RATES

By Ramesh C. Gupta, R. Warren. 2001

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The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval (2018, background): “If h(x) increases in a neighbourhood of zero and h′(x1) ≥ 0 (h′(x1) 0), then h(x) is increasing (increasing-decreasing-increasing) (Gupta and Warren 2001).”
Modelling lifetimes by quantile functions using Parzen's score function (2012, methodology): “It may be noted that the J (u) defined in the previous section is equivalent to the function (when we set x = Q(u)) η(x) = −f ′(x) f (x) used by Glaser [13] and Gupta and Warren [14], in developing criteria for distinguishing increasing (decreasing) –”
Bathtub-shaped failure rate functions (2009, unknown): “8 Gamma mixture distribution Gupta and Warren (2001) examined the mixture of gamma distributions specified by the pdf f (x) = px α1−1 exp (−x/β) βα1 (α1) + (1− p)x α2−1 exp (−x/β) βα2 (α2) for x > 0, α1 > 0, α2 > 0, β > 0 and 0 < p < 1.”