# Beta Geometric Distribution (Type I Geometric)

## What is the Beta Geometric Distribution?

The Beta Geometric distribution is a unique type of distribution. We can think about it as being composed of two pieces: the probability that success will occur, and what’s known as shape parameters α and β which must always be positive numbers. This combination creates an incredibly useful tool in mathematical modelling for both application to real world scenarios, or simply analysing data points efficiently

## Usage

It is well established that the beta binomial model, originally developed by Porter and Park (1964), can be used to accurately predict the number of failures prior to a successful outcome. This makes it particularly useful for fecundity research in population dynamics as waiting time to conception easily follows this pattern. It has also been widely adopted elsewhere where success needs multiple attempts before one succeeds such as process control or other fields involving probability distributions.

## Difference Between Beta Geometric Distribution and Geometric Distribution

While the Geometric distribution assumes a constant probability of success for each trial, the Beta-Geometric model extends this by allowing flexibility in how probabilities change from one trial to another.

## 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
Wolfram. WaringYuleDistribution.