0
|
8921 Views
|
2 Replies
|
2 Total Likes
View groups...
Share
GROUPS:

Calculate the distribution of the sum of two distributions in W|A?

Posted 8 years ago
 I would like to query wolfram alpha to provide the distribution for the sum of two distributions, namely: - g is normal with mean=6% and sd=1%, and - x is exponential with lambda = 1% What is the query needed to be written. Apparently wolfram alpha interprets each distribution correctly but not the sum. I tried: "probability distribution function of g+x, if g is normal with mean=6% and sd=1% and x is exponential with lambda = 1%"
2 Replies
Sort By:
Posted 8 years ago
 Current versions of Mathematica enable an even more direct solution than Craig's, although possibly not as instructive In[12]:= PDF[ TransformedDistribution[ x + y, {x \[Distributed] NormalDistribution[\[Mu], \[Sigma]], y \[Distributed] ExponentialDistribution[\[Lambda]]}]][z] Out[12]= 1/2 E^( 1/2 \[Lambda] (-2 z + 2 \[Mu] + \[Lambda] \[Sigma]^2)) \[Lambda] Erfc[(-z + \[Mu] + \ \[Lambda] \[Sigma]^2)/(Sqrt[2] \[Sigma])] 
Posted 8 years ago
 Hello I am not sure what the Alpha Query would be.However, if you have access to Mathematica, I believe that this is how would do it--and how to think about it (assuming I understand your question correctly:Derivative of the cumulative distribution (ignoring the the fundamental theorem of calculus for a minute) pdf = D[Integrate[ PDF[NormalDistribution[m, sd], x] + PDF[ExponentialDistribution[decay], x], {x, -Infinity, y}, Assumptions -> Element[y, Reals] && sd > 0 && decay > 0], y] Which gives you an expected (remembering the fundamental theorem), but not very exciting unormalized result: pdf = Simplify[pdf] Remembering to normalize norm = Integrate[pdf, {y, -Infinity, Infinity}, Assumptions -> sd > 0 && decay > 0] We recognize an additional fact about the above by looking at ever-helpful mathworld: http://mathworld.wolfram.com/Erfc.html pdf = Simplify[ pdf/norm] 
Community posts can be styled and formatted using the Markdown syntax.