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The survival function is also known as the survivor function [2] or reliability function. [3] The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime ...
That is, the survival function is the probability that the time of death is later than some specified time t. The survival function is also called the survivor function or survivorship function in problems of biological survival, and the reliability function in mechanical survival problems.
Unlike the more commonly used Weibull distribution, it can have a non-monotonic hazard function: when >, the hazard function is unimodal (when ≤ 1, the hazard decreases monotonically). The fact that the cumulative distribution function can be written in closed form is particularly useful for analysis of survival data with censoring . [ 9 ]
An example of a Kaplan–Meier plot for two conditions associated with patient survival. The Kaplan–Meier estimator, [1] [2] also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a ...
The survival function of the κ-Logistic distribution represents the κ-deformation of the Fermi-Dirac function, and becomes a Fermi-Dirac distribution in the classical limit . [ 1 ] The κ -Logistic distribution is a generalization of the κ -Weibull distribution when λ = 1 {\displaystyle \lambda =1} .
This is the survival function for Weibull distribution. For α = 1, it is same as the exponential distribution. Another famous example is when the survival model follows Gompertz–Makeham law of mortality. [2] In this case, the force of mortality is = +
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In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution.