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Format: VoseDirichlet({ai})
The Dirichlet distribution is a multivariate distribution whose components all takes values on (0,1) and which sum to one.
The Dirichlet distribution is used in modeling probabilities, prevalence of fractions where there are multiple states to consider. It is the multinomial extension to the beta distribution for a binomial process.
You have the results of a survey conducted in the premises of a retail outlet. The age and sex of 500 randomly selected shopopers were recorded:
<25 years, male: 38 people
25 to < 40 years, male: 72 people
> 40 years, male: 134 people
<25 years, female: 57 people
25 to < 40 years, female: 126 people
> 40 years, female: 73 people
In a manner analogous to the beta distribution, by adding 1 to each number of observations we can estimate the fraction of all shoppers to this store that are in each category as follows:
=VoseDirichlet({38+1,72+1,134+1,57+1,126+1,73+1})
The Dirichlet then returns the uncertainty about the fraction of all shoppers that are in each group.
A review of 1000 companies that were S&P AAA rated last year in your sector shows their rating one year later:
AAA: 908
AA: 83
A: 7
BBB or below: 2
If we assume that the market has similar volatilities to last year, we can estimate the probability that a company rated AAA now will be in each state next year as:
=VoseDirichlet({908+1,83+1,7+1,2+1})
The Dirichlet then returns the uncertainty about these probabilities.
VoseDirichlet generates values from this distribution
VoseDirichletProb returns the probability density or cumulative distribution function for this distribution
VoseDirichletProb10 returns the log10 of the probability density or cumulative distribution function
