How to obtain exponential equation parameter from probplot function?

I would like to find the function (or equation) of the reference black dashed line that represents the theoretical exponential distribution, in order to work on data that diverge from that line.

Akira Agata 2019-5-30

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If my uderstanding is correct, you have data vector (e.g N-by-1 array) data, and want to estimate exponential distribution parameter a and b in the equation f(x) = a*exp(b*x).

It seems that the following is one possible step to estimate a and b.

% Sample data (e.g 1000-by-1 array)
pd = makedist('Exponential','mu',2);
data = random(pd,1000,1);
% Estimate parameter mu in f(x) = (1/mu)*exp(-x/mu)
pd2 = fitdist(data,'Exponential');
mu = pd2.mu;
% Since a = (1/mu) and b = (-1/mu),
a = 1/mu;
b = -1/mu;

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Answer 2

Jeff Miller 2019-5-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/464407-how-to-obtain-exponential-equation-parameter-from-probplot-function#answer_377137

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For a standard exponential distribution,

probability = 1 - exp(-lambda*x)

where x is the data value and lambda is the parameter of the exponential. I think this is the equation of the black dashed line that you show. (But maybe you some other distribution in mind since you show a function with two parameters, a and b).

The value of lambda used in the previous equation would usually be the maximum likelihood estimate:

lambda_est = 1 / mean(data);

So, your graph makes it look like your data set is more compressed at the high end than would be expected from a true exponential.

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fransec 2019-5-30

Yeah, I think the equation that you proposed represents the black dashed line.

I think that lambda could be 1/mu.

The problem is that I don't know how to plot the probability equation (in plot) over the probability plot, in order to find the intrsection between the two functions...

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