how to fit exponential distribution function on data?
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The vector m follows the truncated exponential equation (F_M) and it is shown by solid black line in figure. I intend to fit an exponential distribution function to data and find the parameter lambda (1/mean). Even though I've used fitdist(x,distname), the fitted exp. dist. shown in dashed line which is way different from the data. here is the code:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/268190/image.jpeg)
M_min=4.5; M_max=8.0;
m=M_min:0.0001:M_max;
a=4.56; b=1.0;
alpha=a*log(10);beta=b*log(10);
nu=exp(alpha-beta*M_min);
F_M=(1-exp(-beta*(m-M_min))) / (1-(exp(-beta*(M_max-M_min)))); % CDF of Mag.
pd = fitdist(m','Exponential');
figure(1); plot(m,1-F_M,'-','linewidth',2);
hold on; plot(m,1-cdf(pd,m),'--');
legend('data','fitted dist')
2 Comments
Answers (2)
Walter Roberson
on 26 Jan 2020
You do not have an exponential distribution. (1 minus an exponential) is not an exponential.
On the other hand if you fit using the equation
a*exp(-b*x)+c
instead of
a*exp(-b*x)
then you get pretty much a perfect fit.
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