SurvivorFunction 2004-07-02 18:21:28 2007-12-18 11:09:39 Definition survival time % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb,amscd} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $Y$ be a random variable with cumulative probability distribution function $F_Y(y)$. Then the \emph{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 \emph{survival time}. The survivor function is the probability of survival beyond time $Y=y$. \textbf{Examples.} The three most commonly used distribution functions for survival time are: \begin{enumerate} \item \PMlinkname{exponential distribution}{ExponentialRandomVariable}, with $S(y)=\exp(-\gamma y).$ \item Weibull distribution, with $S(y)=\exp(-y^{\gamma})$ using the standard Weibull distribution. \item extreme-value distribution, with $S(y)=\exp(-\exp(\displaystyle{\frac{y-\alpha}{\beta}})).$ \end{enumerate}