Convolution of two log normal distributions

Asked by Joshua Woodard

Joshua Woodard (view profile)

on 17 Sep 2019
Latest activity Edited by Bruno Luong

Bruno Luong (view profile)

on 18 Sep 2019
Accepted Answer by Jeff Miller

Jeff Miller (view profile)

Greetings. I am trying to do the convolutions of two lognormal distributions however, I am getting errors. I started to question my method but I cannot find a mistake in my script. Is there a better way? I seem to be getting unexpected numerical values. I would expect like any CDF to approach 1, but this one is not.
%% Convolution of two LogNormal Distributions.
clc
clear all
format long
muX = 9.7224; % For Ni Distribution (X-domain)
sigmaX = 0.3332; % For Ni Distribution (X-domain)
muY = 8.6878; % For Np Distribution (Y-domain)
sigmaY = 0.2454; % For Np Distribution (Y-domain)
t = inf; % Cycles input (would expect an answer of 1 with t = inf.)
fun = @(y,x) exp(-0.5.*((log(x) - muX).^2)./(sigmaX.^2))./(x.*sigmaX.*sqrt(2.*pi)) .* exp(-0.5.*((log(y) - muY).^2)./(sigmaY.^2))./(y.*sigmaY.*sqrt(2.*pi));
P = integral2(fun,-inf,t - 'x',-inf,inf,'RelTol',1e-12,'AbsTol',1e-12)

Release

R2017b

Answer by Jeff Miller

Jeff Miller (view profile)

on 18 Sep 2019

Convolutions are pretty easy to do in Cupid. For example, the following code gives the attached figure
muX = 9.7224; % For Ni Distribution (X-domain)
sigmaX = 0.3332; % For Ni Distribution (X-domain)
muY = 8.6878; % For Np Distribution (Y-domain)
sigmaY = 0.2454; % For Np Distribution (Y-domain)
conv = Convolution(Lognormal(muX,sigmaX),Lognormal(muY,sigmaY));
conv.PlotDens
This might be handy if you also want to try other distributions, try fitting data, etc.

Answer by Image Analyst

Image Analyst (view profile)

on 18 Sep 2019

For convolution, use conv() on your numerical vectors.

Answer by Bruno Luong

Bruno Luong (view profile)

on 18 Sep 2019
Edited by Bruno Luong

Bruno Luong (view profile)

on 18 Sep 2019

LOGNORMAL is defined on (0,Inf) not (-Inf,Inf)
P = integral2(fun,0,t - 'x',0,inf,'RelTol',1e-12,'AbsTol',1e-12)
returns correctly
P =
1.0000