1 / 4

Survival Analysis with Exponential and Gamma Distributions

Learn about exponential and gamma distributions for modeling waiting times and Poisson processes. Calculate probabilities and expected values. Ideal for studying radioactive decay and inter-arrival times.

normandaniel
Download Presentation

Survival Analysis with Exponential and Gamma Distributions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Exponential Distribution • The RV T has an exponential distribution with rate l (for l > 0) if T has the probability density • The mean and standard deviation of T are

  2. Exponential Distribution • The exponential distribution is used to model waiting times for the occurrence of some event (death, failure, mutation, radioactive decay, etc.). • The continuous analog of the geometric distribution. • Models the successive inter-arrival times of a Poisson process in time.

  3. Suppose a particular kind of radioactive atom has a half-life of 2 years. Find • The probability that an atom of this type survives at least 5 years. • The time at which the expected number of atoms is 10% of the original amount.

  4. Gamma Distribution • If Tr is the time of the rth arrival after t = 0 in a Poisson process with rate l, then Tr has the gamma (r, l) distribution with probability density • The mean and standard deviation of Tr are

More Related