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Function Reference: poissfit

statistics: lambdahat = poissfit (x)
statistics: [lambdahat, lambdaci] = poissfit (x)
statistics: [lambdahat, lambdaci] = poissfit (x, alpha)
statistics: [lambdahat, lambdaci] = poissfit (x, alpha, freq)

Estimate parameter and confidence intervals for the Poisson distribution.

lambdahat = poissfit (x) returns the maximum likelihood estimate of the rate parameter, lambda, of the Poisson distribution given the data in x. x must be a vector of non-negative values.

[lambdahat, lambdaci] = poissfit (x) returns the 95% confidence intervals for the parameter estimate.

[lambdahat, lambdaci] = poissfit (x, alpha) also returns the 100 * (1 - alpha) percent confidence intervals of the estimated parameter. By default, the optional argument alpha is 0.05 corresponding to 95% confidence intervals. Pass in [] for alpha to use the default values.

[…] = poissfit (x, alpha, freq) accepts a frequency vector or matrix, freq, of the same size as x. freq typically contains integer frequencies for the corresponding elements in x. freq cannot contain negative values.

Further information about the Poisson distribution can be found at https://en.wikipedia.org/wiki/Poisson_distribution

See also: poisscdf, poissinv, poisspdf, poissrnd, poisslike, poisstat

Source Code: poissfit

Example: 1

  

 ## Sample 3 populations from 3 different Poisson distibutions
 randp ("seed", 2);    # for reproducibility
 r1 = poissrnd (1, 1000, 1);
 randp ("seed", 2);    # for reproducibility
 r2 = poissrnd (4, 1000, 1);
 randp ("seed", 3);    # for reproducibility
 r3 = poissrnd (10, 1000, 1);
 r = [r1, r2, r3];

 ## Plot them normalized and fix their colors
 hist (r, [0:20], 1);
 h = findobj (gca, "Type", "patch");
 set (h(1), "facecolor", "c");
 set (h(2), "facecolor", "g");
 set (h(3), "facecolor", "r");
 hold on

 ## Estimate their lambda parameter
 lambdahat = poissfit (r);

 ## Plot their estimated PDFs
 x = [0:20];
 y = poisspdf (x, lambdahat(1));
 plot (x, y, "-pr");
 y = poisspdf (x, lambdahat(2));
 plot (x, y, "-sg");
 y = poisspdf (x, lambdahat(3));
 plot (x, y, "-^c");
 xlim ([0, 20])
 ylim ([0, 0.4])
 legend ({"Normalized HIST of sample 1 with λ=1", ...
          "Normalized HIST of sample 2 with λ=4", ...
          "Normalized HIST of sample 3 with λ=10", ...
          sprintf("PDF for sample 1 with estimated λ=%0.2f", ...
                  lambdahat(1)), ...
          sprintf("PDF for sample 2 with estimated λ=%0.2f", ...
                  lambdahat(2)), ...
          sprintf("PDF for sample 3 with estimated λ=%0.2f", ...
                  lambdahat(3))})
 title ("Three population samples from different Poisson distibutions")
 hold off
plotted figure