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<p>There are two notable differences. First, the distribution statement will check the inputs to make sure both <code>lambda</code> is positive and <code>y</code> is non-negative (which includes checking that neither is the special not-a-number value).</p>
<p>The second difference is that if <code>lambda</code> is not a parameter, transformed parameter, or local model variable, the distribution statement is clever enough to drop the <code>log(lambda)</code> term. Thi