After studying about the beta distribution I understood that the beta density function is used to find the densities for the probabilities. Densities may range from 0 to inf. That is if the density of any probability value is more we can say that the probability value is most likely to occur. But when coming to CDF of the beta distribution function, its output is also a probability. If the input and output both are probabilities, what should I understand? "The probability of the occurrence of the probability is say some 0.8?" This is what I understood. Is this correct? What should I do to find the probabilities (not cumulative probabilities) rather than the densities using beta distribution?

I am using beta distribution in Bayesian networks as prior my posterior for each node is defined as betapdf(X+success, Y+failure) whose output is density not the probability. Now I need to find the joint probability for the network. How can I do that? For extra information see this link: how to find the joint probability for a Bayesian network?

  • $\begingroup$ Please note that the beta distribution can be used for anything constrained in $[0,1]$, so the inputs are not necessarily probabilities. Currently it is somewhat unclear whether you are asking about interpretations in the beta-binomial model, or about what the pdf and cdf are (I guess the former). Could you add information about what you are using the beta distribution for. Besides clarifying the question, adding this explanation may help answerers to know how much you already understand what is going on. $\endgroup$ Sep 9, 2017 at 6:27
  • $\begingroup$ I am using beta distribution in bayesian networks as prior my posterior for each node is defined as betapdf(X+success, Y+failure) whose out put is density not the probability.now i need to find the joint probability for the network.how can i do that for extra information see this link stats.stackexchange.com/questions/302209/… $\endgroup$ Sep 9, 2017 at 7:11

1 Answer 1


The inputs are never probabilities to either of those functions. Only the outputs are. The density gives the relative likelihood of the RV being x (analogous to the probability of being equal to x in mass functions), the cumulative distribution function the probability of being less than or equal to x (like the name implies)

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    $\begingroup$ The question is most likely asking about the beta-binomial model where the beta distribution is used for a parameter that is a probability $\endgroup$ Sep 9, 2017 at 6:24
  • $\begingroup$ p(θ) =(Γ(a+b)/Γ(a)Γ(b))*(θ^ a−1)((1−θ )^b−1). In this density function if we fix a and b values only input is the random variable theta that ranges from 0 to 1 that is it is probability. so we are finding the densities for the probabilities. here how can the output be a probability please explain me. $\endgroup$ Sep 9, 2017 at 6:26
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    $\begingroup$ It's not. It's a number from 0,1. Not necessarily a probability. $\endgroup$
    – Dale C
    Sep 9, 2017 at 6:28
  • $\begingroup$ thank u Tilefish Poele could please answer my another question in this link stats.stackexchange.com/questions/302209/… and also please tell me what is the output limits of the joint distribution. $\endgroup$ Sep 9, 2017 at 6:41

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