Lifetime Distribution Identities

Five ways of representing the distribution of a continuous nonnegative random variable T are used extensively in the reliability literature: the probability density function, the reliability (survivor function), the hazard rate, the cumulative hazard function, and the mean residual life function. Properties, identities, and intuitive interpretations of the five representations are discussed. Several examples are given. Although there are other functions, such as normalized mean residual life for studying replacement policies, these five distribution representations have surfaced as vehicles for representing a lifetime distribution. The choice of which distribution representation to use depends on whether -1. The representation has a tractable form 2. Intuition is gained concerning the distribution by seeing a plot of the representation.