how to fit exponential distribution function on data?

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:

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')

[Walter Roberson]

a and b are not defined in the third line.

[Mos_bad]

just editted. thanks for pointing that out.

Answer 1

[Walter Roberson]

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.

[Mos_bad]

All I want to do is to devide vertical axis to 1000 intervals and pick a random value of magnitude (horizental axis) at each interval. Kind of Latin hypercube sampling.

Answer 2

[Image Analyst]

See my attached demo.