  # Beta Geometric Distribution (Type I Geometric)

## What is the Beta Geometric Distribution?

The beta geometric distribution (also called the Type I Geometric) is a type of geometric distribution, where the probability of success parameter, p, has a Beta distribution with shape parameters alpha(α) and beta(β); both shape parameters are positive (α > 0 and β > 0). It is a type of compound distribution.

## Usage

The distribution often models the number of failures that will happen in a binomial process before the first observed success. The probability of success is the mean of the distribution, given by the formula α / (α + β). This particular usage is often called the shifted beta binomial.

One particular use often cited is with fecundity in the population, i.e. the number of failures before a successful pregnancy. In fact, the model was originally developed by Porter and Park (1964, as cited in American Statistical Association., 1988) to model this exact scenario: waiting time to conception. It is also used in various other population studies and in process control.

## Difference Between Beta Geometric Distribution and Geometric Distribution

The main difference between the geometric and the Beta Geometric is that p remains constant with the geometric and changes with the beta geometric.

## Similar Distributions

The Yule distribution is a special case of the beta geometric distribution, when β = 1 (King, M, 2017).

## References

American Statistical Association (1988). Proceedings of the Social Statistics Section.
ing, M. (2017). Statistics: A Practical Approach for Process Control Engineers. John Wiley and Sons.
NIST. BGEPDF. Retrieved November 12, 2019 from: https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/bgepdf.htm
R Documentation. Betageom. Retrieved November 12, 2019 from: https://www.rdocumentation.org/packages/VGAM/versions/1.1-1/topics/Betageom

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