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Jul
2
awarded  Curious
Jan
24
comment What is the expectation of the product of two random variables of Dirichlet distribution?
I apologise for my incorrect edit. I thought you use $\alpha_i = \alpha - \alpha_j$ and $\alpha \Gamma(\alpha) = \Gamma(\alpha+1)$ to get the second step of $E(X_i \log X_i)$
Jan
24
revised What is the expectation of the product of two random variables of Dirichlet distribution?
I added more explanations to explain the steps
Jan
24
suggested approved edit on What is the expectation of the product of two random variables of Dirichlet distribution?
Jan
24
comment What is the expectation of the product of two random variables of Dirichlet distribution?
Whoa! Thank you so much! You are a genius. Do you have any recommendations for a good book on Dirichlet distribution? I could not find any references that talk about joint Dirichlet distribution.
Jan
24
accepted What is the expectation of the product of two random variables of Dirichlet distribution?
Jan
24
comment What is the expectation of the product of two random variables of Dirichlet distribution?
can you show me how? Thanks!
Jan
24
revised What is the expectation of the product of two random variables of Dirichlet distribution?
added 9 characters in body
Jan
24
revised What is the expectation of the product of two random variables of Dirichlet distribution?
edited title
Jan
24
comment What is the expectation of the product of two random variables of Dirichlet distribution?
Thank you very much for your answer. Do you have the form for $E[X_i \ln(X_j)]$?
Jan
24
revised What is the expectation of the product of two random variables of Dirichlet distribution?
added 584 characters in body
Jan
24
comment What is the expectation of the product of two random variables of Dirichlet distribution?
@Lost1 I apologise for the poor English, I have amended the question. My main question is how to derive $E[X_i \ln(X_j)]$
Jan
24
revised What is the expectation of the product of two random variables of Dirichlet distribution?
added 2 characters in body; edited title
Jan
23
asked What is the expectation of the product of two random variables of Dirichlet distribution?
Sep
23
comment How to prove that the product of a decreasing monotonic function and a strictly increasing monotonic function is a concave function?
@Oleg567 It is possible. Consider segment [0,1], and functions $f(x) = x, g(x) = e^{-x/5}$
Sep
20
asked How to prove that the product of a decreasing monotonic function and a strictly increasing monotonic function is a concave function?
Sep
18
comment Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points
@JonasMeyer I mean to say that the optimal point is a local maximum. My mistake in confusing turning point to be local maximum
Sep
18
comment Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points
Thank you for your clarifications, I am sorry for mistaken turning point to be local maximum, which I was asking.
Sep
18
revised Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points
deleted 47 characters in body
Sep
18
comment Can the product of an increasing monotonic function and a strictly increasing monotonic function have turning points
Great answer! Is there a set of conditions that need to be fulfilled in order to ensure $h$ has a point of inflection?