This paper focuses on modeling surrender time for policyholders in the context of life insurance. In this setup, a large lapse rate at the first months of a contract is often observed, with a decrease in this rate after some months. The modeling of the time to cancelation must account for this specific behavior. Another stylized fact is that policies which are not canceled in the study period are considered censored. To account for both censoring and heterogeneous lapse rates, this work assumes a Bayesian survival model with a mixture of regressions. The inference is based on data augmentation allowing for fast computations even for datasets of over millions of clients. Moreover, frequentist point estimation based on Expectation–Maximization algorithm is also presented. An illustrative example emulates a typical behavior for life insurance contracts, and a simulated study investigates the properties of the proposed model. A case study is considered and illustrates the flexibility of our proposed model allowing different specifications of mixture components. In particular, the observed censoring in the insurance context might be up to $50\%$ of the data, which is very unusual for survival models in other fields such as epidemiology. This aspect is exploited in our simulated study.

Based on data from low elevation lake sites, previous studies have suggested three quantitative relationships related to summer (December, January and February) air temperatures in the Dry Valleys of Antarctica: i) decrease with altitude at the dry lapse rate of 9.8°C km-1, ii) increase with distance from the coast at a rate of 0.09°C km-1, and iii) degree-days above freezing during the summer months is logarithmically proportional to the maximum summer air temperature. Here, we tested the first two of these rules at high elevation sites in Upper Wright Valley. Direct measurements confirmed that the summer lapse rate followed the dry lapse rate. For the three furthest stations, Tyrol Valley, Mount Fleming and Horseshoe Crater, the average difference between the measurements and the predicted summer monthly averages are -2.1±1.4°C, -0.5±1.0°C and -0.4±0.9°C, respectively. By contrast, at Linnaeus Terrace (54 km from the coast) the monthly average is warmer than predicted by several degrees: +4.3±1.3°C. The inland temperature gradient at these high elevation sites may result from sunlight effects rather than coastal wind as previously shown for the lower valleys. The warm conditions observed c. 50 km from the coast may reflect a zone affected by both sunlight and coastal wind.