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Homesurvivor function

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# survivor function

Let $Y$ be a random variable with cumulative probability distribution function $F_{Y}(y)$. Then the *survivor function* $S(y)$ is defined to be:

$S(y)=1-F_{Y}(y)=P(Y\geq y).$ |

The random variable $Y$ is often called the *survival time*.

The survivor function is the probability of survival beyond time $Y=y$.

Examples. The three most commonly used distribution functions for survival time are:

1. exponential distribution, with $S(y)=\exp(-\gamma y).$

2. Weibull distribution, with $S(y)=\exp(-y^{{\gamma}})$ using the standard Weibull distribution.

3. extreme-value distribution, with $S(y)=\exp(-\exp(\displaystyle{\frac{y-\alpha}{\beta}})).$

Defines:

survival time

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Definition

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## Mathematics Subject Classification

62N99*no label found*62P05

*no label found*

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