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I have a family of probability distributions, indexed by elements in $\mathcal I =\mathbb N \times [0,1] \times [0,1]$. For each $(A,B,C) \in \mathcal I$ I know how to define the corresponding distribution $\mathcal D_{A,B,C}$.

dist := 
   ProbabilityDistribution[
   PDF[BinomialDistribution[A, y*B + (1 - y)*0.5], x]   
   PDF[BernoulliDistribution[C], y], 
   {x, 0, A, 1}, 
   {y, 0, A, 1}];

What I want is to define a probability distribution with parameters, so that fixing parameters n,p,q will yield $\mathcal D_{A,B,C}$.

I have tried the obvious, e.g.

dist[n_,p_,q_] := 
   ProbabilityDistribution[
   PDF[BinomialDistribution[n, y*p + (1 - y)*0.5], x]   
   PDF[BernoulliDistribution[q], y], 
   {x, 0, n, 1}, 
   {y, 0, n, 1}];

But I get an error message of the form SetDelayed::write: Tag ProbabilityDistribution in...is Protected.

I'm thinking there's some simple solution I don't know about (I'm new to Mathematica). I have also tried this (I don't know whether it amounts to the same thing):

dist[n_, p_, q_] := 
 ProbabilityDistribution[
 PDF[BinomialDistribution[i, y*j + (1 - y)*0.5], x] 
 PDF[BernoulliDistribution[k], y], 
 {x, 0, i, 1}, 
 {y, 0, i, 1}] /. {i -> n, j -> p, k -> q};
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    – bbgodfrey
    Aug 15, 2015 at 14:53
  • $\begingroup$ The lines you say have SetDelayed::write message, they run fine for me on MMA 10.2… $\endgroup$
    – Patrick Stevens
    Aug 15, 2015 at 15:11
  • 2
    $\begingroup$ Mathematica will evaluate dist before dist[...], so the SetDelayed error is because your dist[n_,p_,q_] := ... statement is becoming ProbabilityDistribution[...][n_,p_,q_] := ... when evaluated. Does it work if you ClearAll[dist] first? $\endgroup$
    – mfvonh
    Aug 15, 2015 at 15:12
  • 1
    $\begingroup$ Have you looked at ProductDistribution[]? $\endgroup$
    – J. M.'s eventual burnout ♦
    Aug 15, 2015 at 15:14
  • $\begingroup$ @mfvonh, you are correct. Rookie mistake, I suppose! $\endgroup$
    – apc
    Aug 15, 2015 at 15:22

1 Answer 1

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I just needed to do ClearAll[dist] first, as mfvonh pointed out in the comments.

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  • $\begingroup$ Do you mean ClearAll[dist] (capitalization)? $\endgroup$
    – Michael E2
    Aug 15, 2015 at 18:51
  • $\begingroup$ Yes, thank you. $\endgroup$
    – apc
    Aug 15, 2015 at 18:53

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