China 
Africa 
Explore chapters and articles related to this topic
Gradient boosting machines
Published in Brandon M. Greenwell, Tree-Based Methods for Statistical Learning in R, 2022
The Cox PH model is one of the most widely used models for the analysis of survival data. It is a semi-parametric model in the sense that it makes a parametric assumption regarding the effect of the predictors on the hazard function (or hazard rate) at time t, often denoted λt, but makes no assumption regarding the shape of λt; since little is often known about λt in practice, the Cox PH model is quite useful. The hazard rate—also referred to as the force of mortality or instantaneous failure rate—is related to the probability that the event (e.g., death or failure) will occur in the next instant of time, given the event has not yet occurred [Harrell, 2015, Sec. 17.3]; it's not a true probability since λt can exceed one. Studying the hazard rate helps understand the nature of risk of time.
Analyzing Toxicity Data Using Statistical Models for Time-To-Death: An Introduction
Published in Michael C. Newman, Alan W. McIntosh, Metal Ecotoxicology, 2020
Philip M. Dixon, Michael C. Newman
The hazard function, or force of mortality,3 describes the probability of dying as a fraction of the number alive at the beginning of the period. It is mathematically related to the survival function [Equation (3)]. () h(t)=−dlogS(t)/dt=−1S(t)dS(t)dt
Optimal dividends for regulated insurers with a nonlinear penalty
Published in International Journal of Control, 2023
Peng Xu, Zhenlong Chen, Lin Xu
In this section, we illustrate the numerical scheme by an example. We assume that the arrival process of the regulation is a non-homogeneous Poisson process. The arrival intensity of the process at time t is denoted by . Then the distribution function of the arrival time of the regulation τ is of the form We call the function the hazard rate of the insurance company. The function is also known as the force of mortality in actuarial circles. We note that in this case Assume that the force of mortality follows the famous Gompertz–Makeham law of mortality (cf. Gavrilov & Gavrilova, 2011), i.e. the hazard rate is given by and One can find that the exponential distribution is a special case of the Gompertz–Makeham law. Here we adopted the parameter estimation results in Terzioǧlu and Sucu (2015) as the example, which are specified by The numerical result shows that, with the parameters given by (64), the expected lifetime is about 79.04. However, for solvency regulation, this time epoch is too long. Note that the conditional expectation of the residual regulatory time, given current time t, is given by we revise the parameter as Then, the expected regulatory time is 1.1715. In this example, we focus on the impact of regulatory time on the dividend policy. For computation ease, we assume that the claims follow the exponential distribution with mean 1 and set . Then the impact of current time t on the value function is illustrated by Figure 1. The corresponding barrier is shown in Table 1.