P.Mean: Bayesian inference on the geometric distribution  (created 2011-05-22).

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I am interested in modelling accrual patterns in clinical trials. I have developed models for an exponential waiting time, and will develop a comparable model for a Poisson count. Another distribution that could be used for accrual is the geometric distribution.

The geometric distribution is quite simple. It assigns probability to non-negative integers (0, 1, 2, ...) using the following formula.

P[X=k] = p (1-p)^k

It can be thought of as a version of the exponential distribution where the value generated by the exponential distribution is rounded down to an integer value. If Y is an exponential variable, then

P[ k <= Y < (k+1)] = (1-exp(-lambda*(k+1)) - (1-exp(-labmda*k))

= exp(-lambda*k) - exp(-lambda*(k+1))

= exp(-lambda*k) (1 - exp(-lambda))

= q^k (1-q)

where

q = exp(-lambda)

The gamma distribution is a common choice for the prior distribution on lambda. the distribution for q is going to be

Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 United States License. This page was written by Steve Simon and was last modified on 2011-01-01. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Incomplete pages.