Hobbies And Interests
Distribution Function
Beta distribution has two parameters, alpha and beta. Somewhat confusingly, one of the distribution's parameters has the same name as the distribution itself. The distribution function of the beta distribution is P(x) = G(alpha + beta)/G(alpha)*G(beta)*(1-x)^(beta-1)*x^(alpha-1), where P(x) is the probability of x, G is the gamma function, which is similar to the factorial function, and alpha and beta are parameters.
A Prior in Bayesian Statistics
Bayesian statistics uses prior beliefs about a subject as part of the analysis. For example, you may believe that the average adult male weighs 170 pounds, but you also believe that they vary in their weight. In order to model these prior beliefs, your prior beliefs about a variable must be modeled. Because of its great flexibility, the Beta distribution is often used to model prior beliefs. By choosing alpha and beta, almost any belief structure can be modeled.
Mean and Variance
A distribution's mean is the arithmetic average. Beta distribution's mean is
alpha/(alpha+beta). The distribution's variance is a measure of how spread out the distribution is. Beta distribution's variance is alpha*beta/(alpha+beta)^2*(alpha+beta+1). For example, if alpha is 1 and beta is .25, the mean will be 1/1.25 = 0.8 and the variance will be 1*.25/2*(1+.25+1) = .25/2*2.25 = .25/4.5 = 0.056. However, it is best to look at Beta distribution graphs to fully appreciate its flexibility.
Use in Project Management
In project management, it is often necessary to estimate the likely amount of time it will take to complete a task and the Beta distribution is often used for this purpose. Given the minimum, maximum and estimated completion time, you can calculate the parameters for a Beta distribution of the appropriate shape. You can also do this given the mean and standard deviation of the amount of time.