MATLAB: How to get Gamma pdf from gamma cdf

gamma pdf. gamma cdf

Hello, everybody.

My question is this. i have a gamma cdf( cumulative distribution function) and corresponding x, now i want to get gamma pdf( probability distribution function) from the cdf data.

I have a the cdf and the corresponding x. such as:

 peak     10%     30%     50%    70%   90% ///                
 49        17     42      64     91    136 ///                 
 53        18     45      69     97    145

the first row is the cdf,this second and third row are the corresponding x, in meters.

I need get probability from 0 to 135m the step can be set 5 meter at interval.

How can I do this? thanks.

Best Answer

I think the page http://www.mathworks.com/help/stats/examples/fitting-a-univariate-distribution-using-cumulative-probabilities.html explains the approach you could take. You'll probably want to read the whole page, but the most relevant part is probably the section entitled "Non-Location-Scale Families", where gamma fitting is discussed explicitly.

Related Solutions

MATLAB: How to go about finding the standard normal probability based on the z-score

doc normcdf
doc normpdf

When you know what you want but not sure the name, try something like

>> lookfor normal
realmin                        - Smallest positive normalized floating point number.
randn                          - Normally distributed pseudorandom numbers.
sprandn                        - Sparse normally distributed random matrix.
surfnorm                       - Surface normals.
isonormals                     - Isosurface normals.
cde                            - cd elliptic function with normalized complex argument.
sne                            - sn elliptic function with normalized complex argument.
addfreqcsmenu                  - Add a cs menu to switch between linear and normalized frequency
convertfrequnits               - converts between Normalized, Hz, kHz, etc
histfit                        - Histogram with superimposed fitted normal density.
jbtest                         - Jarque-Bera hypothesis test of composite normality.
lhsnorm                        - Generate a latin hypercube sample with a normal distribution
logncdf                        - Lognormal cumulative distribution function (cdf).
lognfit                        - Parameter estimates and confidence intervals for lognormal data.
logninv                        - Inverse of the lognormal cumulative distribution function (cdf).
lognlike                       - Negative log-likelihood for the lognormal distribution.
lognpdf                        - Lognormal probability density function (pdf).
lognrnd                        - Random arrays from the lognormal distribution.
lognstat                       - Mean and variance for the lognormal distribution.
mvncdf                         - Multivariate normal cumulative distribution function (cdf).
mvnpdf                         - Multivariate normal probability density function (pdf).
mvnrnd                         - Random vectors from the multivariate normal distribution.
normcdf                        - Normal cumulative distribution function (cdf).
normfit                        - Parameter estimates and confidence intervals for normal data.
norminv                        - Inverse of the normal cumulative distribution function (cdf).
normlike                       - Negative log-likelihood for the normal distribution.
normpdf                        - Normal probability density function (pdf).
normplot                       - Displays a normal probability plot.
normrnd                        - Random arrays from the normal distribution.
normspec                       - Plots normal density between specification limits.
normstat                       - Mean and variance for the normal distribution.
logn3fit                       - Fit a 3-param lognormal dist'n using cumulative probabilities.
wgtnormfit                     - Fitting example for a weighted normal distribution.
wgtnormfit2                    - Fitting example for a weighted normal distribution (log(sigma) parameterization).
>>

Judicious search terms help but seeing the list of things related to "normal" lets you find the two functions of interest (plus a lot more depending upon which toolboxes are available, maybe) that might be of use/interest...

MATLAB: CDF of gamma distribution

I'm not sure how you are calling it, but you should get the same result with gamcdf and gammainc, provided you scale the x vector by the value of your theta parameter prior to calling gammainc

   x = 0:0.01:20;
   k = 2;  % shape parameter
   theta = 3; % scale parameter
   F = gamcdf(x,k,theta);
   plot(x,F,'b');
   hold on;
   x1 = x./theta;  %scale x axis by theta
   Z = gammainc(x1,k);
   plot(x,Z,'k')
   max(abs(Z-F))

Best Answer

Related Solutions

MATLAB: How to go about finding the standard normal probability based on the z-score

MATLAB: CDF of gamma distribution

Related Question