Finding the best probability distribution given a set of probability distributions.

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Consider a system whose output is a discrete random variable $X$ with probability mass function given by $p_t$. Here $t$ indicates that the distribution $p_t$of the random variable $X$ is a function of time (discrete). Suppose I have obtained a sequence (kind of a time series) of distributions corresponding to $X$, say $D= p_1,....,p_n$. How to find the best distribution $p_X$ that represents the random variable $X$ with respect to an appropriate metric?



Can someone guide me to some metric/results/frameworks in probability and statistics that address my problem?




probability probability-theory statistics probability-distributions statistical-inference




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    The setup is unclear; are you saying that the distribution for $X$ is changing over time, and given its past distributions you want to predict its future ones?
    – Mike Earnest
    Aug 6 at 18:06










  • Yes, exactly! I want to find the distribution which captures the previously observed distributions.
    – Suhan Shetty
    Aug 7 at 6:15














up vote
0
down vote

favorite












Consider a system whose output is a discrete random variable $X$ with probability mass function given by $p_t$. Here $t$ indicates that the distribution $p_t$of the random variable $X$ is a function of time (discrete). Suppose I have obtained a sequence (kind of a time series) of distributions corresponding to $X$, say $D= p_1,....,p_n$. How to find the best distribution $p_X$ that represents the random variable $X$ with respect to an appropriate metric?



Can someone guide me to some metric/results/frameworks in probability and statistics that address my problem?




probability probability-theory statistics probability-distributions statistical-inference




share|cite|improve this question















  • 1




    The setup is unclear; are you saying that the distribution for $X$ is changing over time, and given its past distributions you want to predict its future ones?
    – Mike Earnest
    Aug 6 at 18:06










  • Yes, exactly! I want to find the distribution which captures the previously observed distributions.
    – Suhan Shetty
    Aug 7 at 6:15












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Consider a system whose output is a discrete random variable $X$ with probability mass function given by $p_t$. Here $t$ indicates that the distribution $p_t$of the random variable $X$ is a function of time (discrete). Suppose I have obtained a sequence (kind of a time series) of distributions corresponding to $X$, say $D= p_1,....,p_n$. How to find the best distribution $p_X$ that represents the random variable $X$ with respect to an appropriate metric?



Can someone guide me to some metric/results/frameworks in probability and statistics that address my problem?




probability probability-theory statistics probability-distributions statistical-inference




share|cite|improve this question











Consider a system whose output is a discrete random variable $X$ with probability mass function given by $p_t$. Here $t$ indicates that the distribution $p_t$of the random variable $X$ is a function of time (discrete). Suppose I have obtained a sequence (kind of a time series) of distributions corresponding to $X$, say $D= p_1,....,p_n$. How to find the best distribution $p_X$ that represents the random variable $X$ with respect to an appropriate metric?



Can someone guide me to some metric/results/frameworks in probability and statistics that address my problem?





probability probability-theory statistics probability-distributions statistical-inference





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 6 at 17:36









Suhan Shetty

885




885







  • 1




    The setup is unclear; are you saying that the distribution for $X$ is changing over time, and given its past distributions you want to predict its future ones?
    – Mike Earnest
    Aug 6 at 18:06










  • Yes, exactly! I want to find the distribution which captures the previously observed distributions.
    – Suhan Shetty
    Aug 7 at 6:15












  • 1




    The setup is unclear; are you saying that the distribution for $X$ is changing over time, and given its past distributions you want to predict its future ones?
    – Mike Earnest
    Aug 6 at 18:06










  • Yes, exactly! I want to find the distribution which captures the previously observed distributions.
    – Suhan Shetty
    Aug 7 at 6:15







1




1




The setup is unclear; are you saying that the distribution for $X$ is changing over time, and given its past distributions you want to predict its future ones?
– Mike Earnest
Aug 6 at 18:06




The setup is unclear; are you saying that the distribution for $X$ is changing over time, and given its past distributions you want to predict its future ones?
– Mike Earnest
Aug 6 at 18:06












Yes, exactly! I want to find the distribution which captures the previously observed distributions.
– Suhan Shetty
Aug 7 at 6:15




Yes, exactly! I want to find the distribution which captures the previously observed distributions.
– Suhan Shetty
Aug 7 at 6:15










1 Answer
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I would suggest using recurrent neural network if you have enough data. look for relative entropy or KL distance it might help.






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  • Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
    – Suhan Shetty
    Aug 7 at 6:19










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










I would suggest using recurrent neural network if you have enough data. look for relative entropy or KL distance it might help.






share|cite|improve this answer





















  • Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
    – Suhan Shetty
    Aug 7 at 6:19














up vote
1
down vote



accepted










I would suggest using recurrent neural network if you have enough data. look for relative entropy or KL distance it might help.






share|cite|improve this answer





















  • Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
    – Suhan Shetty
    Aug 7 at 6:19












up vote
1
down vote



accepted







up vote
1
down vote



accepted






I would suggest using recurrent neural network if you have enough data. look for relative entropy or KL distance it might help.






share|cite|improve this answer













I would suggest using recurrent neural network if you have enough data. look for relative entropy or KL distance it might help.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 6 at 18:04









Alireza Moradzadeh

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  • Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
    – Suhan Shetty
    Aug 7 at 6:19
















  • Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
    – Suhan Shetty
    Aug 7 at 6:19















Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
– Suhan Shetty
Aug 7 at 6:19




Well, I have something like 10 to 15 instance of distributions. NN may not apply here.
– Suhan Shetty
Aug 7 at 6:19












 

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