Analytical hazard representations for use in reliability, mortality, and simulation studies

The analysis of some algorithms for generating random variates with a given hazard rate

“…Since standard thinning has the property that E ( N ) = p = E ( h ( 0 ) X ) when a constant dominating curve is used for a DHR distribution we expect that there should be inequalities linking E ( N ) for dynamic thinning and p,, that improve over E ( N ) 5 p. Without attempting to obtain a "sharp" inequality, we are able to show that E ( N ) cannot increase faster than gk: then we can write the following inclusion of events:…”

An integrated lack of memory characterization of the exponential distribution

“…These distributions have recently received special attention in statistical literature (see, e.g. Gaver and Acar [5]). …”

Transformation of the bathtub failure rate data in reliability for using Weibull-model analysis

“…In order to deal with problems indicating bathtub-shaped failure rates, many specialized distributions have been proposed, these include Stacy's [35] generalized gamma, Prentice's generalized F distribution [30], the four-parameter family introduced by Graver and Acar [13], a threeparameter (IDB) family proposed by Hjorth [15], a three parameter family studied by Glaser [12] and a two-parameter family introduced by Haupt and Schabe [14]. A reasonable comprehensive account of the models for bathtub-shaped failure rates was given by Rajarshi and Rajarshi [31].…”