Mixing
Discrete distribution where mgf exists only at zero but all moments are finite
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Does such a distribution exist and if it does, what does it look like? For the continuous case, there is the log-normal distribution, so my gut says there must be an analogous discrete distribution but I'm having a hard time constructing it.
probability probability-theory probability-distributions
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
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add a comment |
$begingroup$
Does such a distribution exist and if it does, what does it look like? For the continuous case, there is the log-normal distribution, so my gut says there must be an analogous discrete distribution but I'm having a hard time constructing it.
probability probability-theory probability-distributions
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
$endgroup$
add a comment |
$begingroup$
Does such a distribution exist and if it does, what does it look like? For the continuous case, there is the log-normal distribution, so my gut says there must be an analogous discrete distribution but I'm having a hard time constructing it.
probability probability-theory probability-distributions
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
$endgroup$
Does such a distribution exist and if it does, what does it look like? For the continuous case, there is the log-normal distribution, so my gut says there must be an analogous discrete distribution but I'm having a hard time constructing it.
probability probability-theory probability-distributions
probability probability-theory probability-distributions
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
asked Jan 20 at 12:31
Micky MesserMicky Messer
287
287
add a comment |
add a comment |
1 Answer
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Discrete example, based on your continuous one: $P(X=n)proptofrac{1}{|n|}exp-frac{ln^2 |n|}{2}$ for integers $nne 0$, the proportionality constant determined by unitarity. Proof of validity is an easy exercise with the integral test for convergence. I've made the distribution symmetric to ensure even negative-real-part arguments for the mgf don't let it converge.
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
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1 Answer
1
active
oldest
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1 Answer
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active
oldest
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active
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votes
$begingroup$
Discrete example, based on your continuous one: $P(X=n)proptofrac{1}{|n|}exp-frac{ln^2 |n|}{2}$ for integers $nne 0$, the proportionality constant determined by unitarity. Proof of validity is an easy exercise with the integral test for convergence. I've made the distribution symmetric to ensure even negative-real-part arguments for the mgf don't let it converge.
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
$endgroup$
add a comment |
$begingroup$
Discrete example, based on your continuous one: $P(X=n)proptofrac{1}{|n|}exp-frac{ln^2 |n|}{2}$ for integers $nne 0$, the proportionality constant determined by unitarity. Proof of validity is an easy exercise with the integral test for convergence. I've made the distribution symmetric to ensure even negative-real-part arguments for the mgf don't let it converge.
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
$endgroup$
add a comment |
$begingroup$
Discrete example, based on your continuous one: $P(X=n)proptofrac{1}{|n|}exp-frac{ln^2 |n|}{2}$ for integers $nne 0$, the proportionality constant determined by unitarity. Proof of validity is an easy exercise with the integral test for convergence. I've made the distribution symmetric to ensure even negative-real-part arguments for the mgf don't let it converge.
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
$endgroup$
Discrete example, based on your continuous one: $P(X=n)proptofrac{1}{|n|}exp-frac{ln^2 |n|}{2}$ for integers $nne 0$, the proportionality constant determined by unitarity. Proof of validity is an easy exercise with the integral test for convergence. I've made the distribution symmetric to ensure even negative-real-part arguments for the mgf don't let it converge.
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
answered Jan 20 at 12:53
J.G.J.G.
28.7k22845
28.7k22845
add a comment |
add a comment |
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