CODEWITHSUNDEEP
matlabexponential
user2953016
user2953016

Reputation: 21

Best exponential function algorithm, coefficients and errors?

I have experimental data for exponential distribution a*exp(b*x). the objetive is to find the coefficients a, b and their errors.

I have tried using the function fit(B,C, 'exp1') and got some results.

Currently i'm experimenting problems because some data points in my file have higher error rate due to the nature of the experiment.

The concrete questions are:

  1. Which algorithm or function in Matlab can give the smallest error ?
  2. How can I use/adopt some function in Matlab to put smaller weight (when I calculate coefficients) on data that drastically differ from exponential function ?

Upvotes: 1

Views: 641

Answers (2)

A. Donda
A. Donda

Reputation: 8477

Are you sure you are talking about the exponential distribution? If yes, I'm assuming you computed a histogram and now want to fit a line to the histogram. But that's not the best approach.

First, note that the probability density function of the exponential distribution has only a single parameter, due to the normalization of the pdf. The expression for the density is

lambda * exp(-lambda * x)

Secondly, you do not fit a distribution to data by fitting its pdf to a histogram. There are several approaches to parameter estimation, the most common is "maximum likelihood". According to Wikipedia, the maximum likelihood estimator of lambda is the inverse of the sample mean, or in Matlab notation:

lambda_est = 1 / mean(x)

To get a rough idea whether describing your data by this distribution makes sense, you can then plot the pdf using the estimated parameter over the (normalized) histogram, or over a nonparametric density estimate like that given by ksdensity.

Upvotes: 1

am304
am304

Reputation: 13876

Use the fitoptions argument to specify weights for the fit, or exclude some data points. See the fit documentation for more details.

Upvotes: 1

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