How I can add an exponential fit to my cdfplot?

Hi there,

I have data to be used in a cdfplot as shown below, if I want to add on the plot an exponential fit to the data, what do I need to do, and what is the growth constant of that exponentional

Thanks in advance

z=[
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
    7.1000
    7.2000
    7.7000
    8.2000
    8.8000
    9.0700
    9.7600
   11.2200
   11.2200
   11.4000
   11.6000
   11.8000
   12.3000
   12.8500
   13.3000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.6000
   15.6000
   15.6000
   15.6000
   15.6000
   15.7000
   15.8000
   16.2000
   16.2000
   16.5000
   16.6000
   16.6000
   16.6000
   16.6800
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   17.0600
   17.3000
   17.6000
   17.6000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7700
   17.8000
   18.2000
   18.2900
   18.3200
   18.3300
   19.5400
   20.6000
   20.8400
   21.1000
   24.1000
   24.4000
   25.6000
   26.4000
   26.5000
   26.5000
   26.5000
   26.5000
   26.5000
   26.5400
   26.5700
   27.0000
   27.1000
   28.0000
   28.0300
   29.3800
   30.0000
   30.0000
   30.0000
   30.0000
   30.0000
   31.0000
   31.0000
   31.0000
   31.0000
   31.0000
   31.1000
   31.1000
   31.1000
   31.1000
   31.1000
   31.3000
   31.4000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3200
   33.3500
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   34.0900
   34.7000
   38.3800
   38.4000
   39.0200
   42.1000
   42.1000
   42.2000
   42.2000
   42.2000
   42.3000
   43.3000
   43.3200
   43.3500
   43.4000
   43.4000
   43.4000
   45.0000
   45.0000
   45.0000
   45.1000
   45.1000
   48.0000
   49.4000
   53.1000
   53.2000
   53.2000
   53.2400
   53.2700
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7300
   65.7000
   65.8000
   65.8200
   66.3000
   70.2000
   70.2000
   70.3000
   70.3000
   70.3000
   70.3400
   70.5000
   72.2000
   74.0000
   77.3000
   77.5000
   77.6000
   78.0000
   89.6000
   90.0000
   90.0000
   90.3000
   90.3000
  113.0000
  113.0000
  113.3000
  113.3000
  113.6300
  203.0000
  203.3700
  203.4000
  203.4000
  203.4000
  203.7000
  203.7000
  203.7000
  203.7000
  204.0000
  204.0400
];
cdfplot(z)

Answer 1

[Davide Masiello]

I guess you could do something like this

load z
x = linspace(0,1,length(z));

fitfunc = fittype(@(A,B,C,x) A*exp(B*x.^C));
x0 = [10 10 0.5];
f = fit(x',z,fitfunc,'StartPoint',x0)

f = 
     General model:
     f(x) = A*exp(B*x.^C)
     Coefficients (with 95% confidence bounds):
       A =       11.04  (9.03, 13.04)
       B =       2.965  (2.789, 3.142)
       C =       3.294  (2.903, 3.685)

coeffvals = coeffvalues(f)

coeffvals = 1×3

11.0363 2.9653 3.2940

plot(f(x),x,'-r',z,x,'b.')
legend('fitted curve','data')

[Torsten]

@Davide Masiello

The underlying probability distribution has 1/4 of its mass in x=0. The exponential should thus start in (0,0.25) approximately which would give a value of 0.25 for A right from the beginning.

[Hozifa]

Thanks all for your contributions, really I am gratful.

@Torsten Do I need to change anything to the code? Thanks

[Davide Masiello]

@Torsten that's a good point, thanks.

@Hozifa, the code would stay the same, except you no longer need A to be an adjustable parameter (i.e., you can just set it to A=0.25)

[Hozifa]

@Davide Masiello,

Dear Davide, I've been trying to edit the value of A, but I am not an expert on Matlab and I could not do it. Could you please let me know how to do it, sorry for any inconvenience.

[Torsten]

z=[
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
         0
    7.1000
    7.2000
    7.7000
    8.2000
    8.8000
    9.0700
    9.7600
   11.2200
   11.2200
   11.4000
   11.6000
   11.8000
   12.3000
   12.8500
   13.3000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.5000
   15.6000
   15.6000
   15.6000
   15.6000
   15.6000
   15.7000
   15.8000
   16.2000
   16.2000
   16.5000
   16.6000
   16.6000
   16.6000
   16.6800
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   16.7000
   17.0600
   17.3000
   17.6000
   17.6000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7000
   17.7700
   17.8000
   18.2000
   18.2900
   18.3200
   18.3300
   19.5400
   20.6000
   20.8400
   21.1000
   24.1000
   24.4000
   25.6000
   26.4000
   26.5000
   26.5000
   26.5000
   26.5000
   26.5000
   26.5400
   26.5700
   27.0000
   27.1000
   28.0000
   28.0300
   29.3800
   30.0000
   30.0000
   30.0000
   30.0000
   30.0000
   31.0000
   31.0000
   31.0000
   31.0000
   31.0000
   31.1000
   31.1000
   31.1000
   31.1000
   31.1000
   31.3000
   31.4000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3000
   33.3200
   33.3500
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   33.4000
   34.0900
   34.7000
   38.3800
   38.4000
   39.0200
   42.1000
   42.1000
   42.2000
   42.2000
   42.2000
   42.3000
   43.3000
   43.3200
   43.3500
   43.4000
   43.4000
   43.4000
   45.0000
   45.0000
   45.0000
   45.1000
   45.1000
   48.0000
   49.4000
   53.1000
   53.2000
   53.2000
   53.2400
   53.2700
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7000
   56.7300
   65.7000
   65.8000
   65.8200
   66.3000
   70.2000
   70.2000
   70.3000
   70.3000
   70.3000
   70.3400
   70.5000
   72.2000
   74.0000
   77.3000
   77.5000
   77.6000
   78.0000
   89.6000
   90.0000
   90.0000
   90.3000
   90.3000
  113.0000
  113.0000
  113.3000
  113.3000
  113.6300
  203.0000
  203.3700
  203.4000
  203.4000
  203.4000
  203.7000
  203.7000
  203.7000
  203.7000
  204.0000
  204.0400
];
x = linspace(0,1,length(z));
fitfunc = fittype(@(B,C,x) 0.25*exp(B*x.^C));
x0 = [10 0.5];
f = fit(x',z,fitfunc,'StartPoint',x0)

f = 
     General model:
     f(x) = 0.25*exp(B*x.^C)
     Coefficients (with 95% confidence bounds):
       B =       6.609  (6.56, 6.658)
       C =      0.9425  (0.8716, 1.013)

coeffvals = coeffvalues(f)

coeffvals = 1×2

6.6089 0.9425

plot(f(x),x,'-r',z,x,'b.')
legend('fitted curve','data')

[Hozifa]

@Torsten, thank you very much, I am really in your debt