The Arctangent Survival Distribution

We present a two-parameter survival distribution that has an upside-down bathtub (UBT, or humped-shaped) hazard function. This distribution provides biostatisticians, reliability engineers, and other statisticians with a second two-parameter UBT model whose closed-form survivor function simplifies the analysis of right-censored data sets. We develop the distribution's probabilistic and statistical properties. Maximum likelihood estimators of the parameters are found using numerical methods. Approximate confidence intervals can be determined by using the observed information matrix or the likelihood ratio statistic. We also give examples in which the arctangent distribution is a reasonable alternative to other common lifetime distributions.