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What is the range in which the dirichlet parameters (alphas) should lie? I saw the condition that alphas must be greater than 0. Then can I have alpha values between 0 and 1?

Anagha Raveendran
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  • The Wikipedia summary is explicit: the criterion is only $\alpha_i\gt 0$. Greater than zero means exactly that; it doesn't also mean less than 1! See https://en.wikipedia.org/wiki/Dirichlet_distribution#/media/File:Dirichlet-3d-panel.png for illustrations of the density for some $\alpha_i$ that exceed $1$. – whuber Jan 08 '18 at 14:21
  • Do you meant that alpha values 0.386 and 0.4935 and 1.266 are wrong? I estimated it by method of moments and the equation derived in a reference of 1992. Can you please suggest me a method to estimate alphas of a dirichlet distribution with equations. I will try again to get parameter values. I am basically not from a statistical ground and new to especially dirichlet distributions and Bayesian analysis. – Anagha Raveendran Jan 09 '18 at 16:57
  • Are any of those values zero or negative? No, so they are consistent with the condition $\alpha_i\gt 0$. – whuber Jan 09 '18 at 17:00
  • Value of each variable lies between 0 and 1. I have three set of observations for each variable. For var1- (0.2, 0.75 and 0.82). For var 2 - (0.2, 0.22 and 0.12). For var3 - (0.6, 0.03 and 0.06). Each set of observations sums to 1. For var 1, I estimated the alpha as 1.266 by the method of moments given by "A. Narayanan,1992, A note on parameter estimation in the multivariate beta distribution".Then I found dirichlet mode for var 1. But I get negative mode as the denominator(2.1455 - 3)is negative. – Anagha Raveendran Jan 10 '18 at 04:53
  • You're using the formula incorrectly. Even the Wikipedia article on the Dirichlet distribution is clear that the mode formula applies only when all parameters equal or exceed $1$. – whuber Jan 10 '18 at 05:18
  • Yes, what you point out is correct. But I have alpha1=1.266, alpha 2 = 0.386, and alpha 3 = 0.4935 for var1, by using the method of moments. and then alpha 1 + alpha 2 + alpha 3 = 2.1455. Then I get mode of var1 as negative and the modes of other two variables as positive as the ' -' sign in denominator and numerator cancels out. But they sums to 1. I also found mean for each variable but they do not create such problems and they also sums to 1. But what we should do in the cases where alphas are less than 1 and summation of alphas are less than K (in this case K=3) to find mode? – Anagha Raveendran Jan 11 '18 at 04:26

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