How to fit the cdf to a function?

Hi there,

I want my code to give the exponential fit as a function of the x-axis values, in my code, the fit function depends on the generated linespace,

Mnay thanks,

clear 
clc
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
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
    0
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    0
    0
    0
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    0
    8.2000
    8.4000
    10.4000
    10.4000
    11.0000
    11.2000
    11.4000
    11.4000
    11.5000
    11.5900
    11.7000
    11.8000
    12.0000
    12.2000
    12.3400
    12.4300
    12.6000
    12.9700
    13.2100
    13.2900
    13.3400
    13.3800
    14.4000
    15.4500
    15.8200
    15.9900
    16.2600
    16.4200
    16.4400
    16.8100
    17.6100
    17.7000
    19.0400
    20.8100
    21.4000
    22.0800
    22.4000
    22.4300
    22.4700
    22.5000
    22.5000
    22.5000
    23.4800
    23.5500
    23.7500
    24.1100
    24.4800
    24.6000
    24.7000
    26.0900
    26.3000
    26.4400
    26.4500
    26.4800
    26.5100
    27.0000
    27.9000
    28.3900
    28.8500
    29.5000
    29.8500
    30.3000
    30.3000
    31.0000
    31.3000
    31.3200
    33.1000
    33.5700
    33.6500
    33.9000
    34.9300
    36.2400
    36.6000
    37.0200
    38.8200
    39.6900
    40.1600
    40.2800
    40.3000
    40.6200
    41.0300
    41.1900
    42.6800
    42.7100
    42.7500
    43.6500
    43.8000
    43.9000
    46.6000
    46.6700
    49.4100
    49.5400
    49.6800
    49.8500
    50.3000
    53.9000
    56.6000
    60.3000
    62.9000
    72.9000
    72.9000
    72.9000
    72.9000
    72.9000
    73.0000
    73.0000
    73.0000
    73.0000
    73.3000
    73.3000
    73.3000
    73.3000
    73.3000
    73.3000
    73.3000
    73.3000
    73.3000
    73.3800
    73.4000
    73.4000
    73.4000
    73.4000
    73.4000
    73.4000
    73.4000
    73.4000
    73.4000
    73.4200
    73.4500
    73.6000
    73.6000
    73.6000
    73.6000
    73.6000
    73.6000
    73.6000
    73.6000
    ];
cdfplot(z)
hold on 
x = linspace(0,1,length(z));
% x=z;
fitfunc = fittype(@(B,C,x) 0.4*exp(B*x.^C));
x0 = [10 0.5];
f = fit(x',z,fitfunc,'StartPoint',x0)
coeffvals = coeffvalues(f)
plot(f(x),x,'-r',z,x,'b.')
% legend('fitted curve','data')
legend('LOS','Exponential fit')

set(findall(gcf,'type','line'),'LineWidth',1)
set(gca,'fontweight','bold','FontSize',12)
xlabel('Inter cluster delay (ns)','fontweight','bold','fontsize',12)
ylabel ('Probability','fontweight','bold','fontsize',12)

Answer 1

[William Rose]

@Hozifa,

[edit: correct spelling and grammar]

I put the data in a text file so it is not in your code. It appears that the data are interpreted as being samples of a random variable, which have been sorted into ascending order.

Your question and the comments in the code indicate you want to fit an exponential distribution to the data:

The max. likelihood estimate (MLE) for lambda is 1/mean(x)

Therefore I have computed the CDF with this estimate, and I have added it to the plot. Of course your data shows signs of thresholding and saturation, which violate the assumptions used in the MLE derivation. Thresholding and saturation are types of data censoring. Google, or search matlab answers, for more info on advanced strategies for fitting censored data, if that is of interest.

In the code below, I computed the MLE and added the corresponding CDF to the plot. This method of fitting does not depend on a generated linespace vector, which was your original concern.

z=load('statdata.txt');
cdfplot(z)
hold on 
x = linspace(0,1,length(z));
fitfunc = fittype(@(B,C,x) 0.4*exp(B*x.^C));
x0 = [10 0.5];
f = fit(x',z,fitfunc,'StartPoint',x0)

f = 
     General model:
     f(x) = 0.4*exp(B*x.^C)
     Coefficients (with 95% confidence bounds):
       B =       5.426  (5.396, 5.456)
       C =       0.582  (0.5531, 0.611)

coeffvals = coeffvalues(f)

coeffvals = 1×2

5.4257 0.5820

lambda=1/mean(z);               %MLE for exponential distribution
cdf_mle=1-exp(-lambda*[1:100]); %CDF using MLE for lambda
plot(f(x),x,'-r',z,x,'b.',[1:100],cdf_mle,'-g')
% legend('fitted curve','data')
legend('','Exponential fit','LOS','MLE')
set(findall(gcf,'type','line'),'LineWidth',1)
set(gca,'fontweight','bold','FontSize',12)
xlabel('Inter cluster delay (ns)','fontweight','bold','fontsize',12)
ylabel ('Probability','fontweight','bold','fontsize',12)