From 3aee2fd43e3059a699af2b63c6f2395e5a55e515 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Wed, 27 Sep 2017 15:06:31 +0100 Subject: First commit on github -- NetBunch 1.0 --- doc/fitmle.1.html | 215 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 215 insertions(+) create mode 100644 doc/fitmle.1.html (limited to 'doc/fitmle.1.html') diff --git a/doc/fitmle.1.html b/doc/fitmle.1.html new file mode 100644 index 0000000..863099c --- /dev/null +++ b/doc/fitmle.1.html @@ -0,0 +1,215 @@ + + + + + + fitmle(1) - Fit a set of values with a power-law distribution + + + + + +
+ + + +
    +
  1. fitmle(1)
    2. +
  2. www.complex-networks.net
    3. +
  3. fitmle(1)
    4. +
+ +

NAME

+

+ fitmle - Fit a set of values with a power-law distribution +

+ +

SYNOPSIS

+ +

fitmle data_in [tol [TEST [num_test]]]

+ +

DESCRIPTION

+ +

fitmle fits the data points contained in the file data_in with a +power-law function P(k) ~ k-gamma, using the Maximum-Likelihood +Estimator (MLE). In particular, fitmle finds the exponent gamma +and the minimum of the values provided on input for which the +power-law behaviour holds. The second (optional) argument tol sets +the acceptable statistical error on the estimate of the exponent.

+ +

If TEST is provided, the program associates a p-value to the +goodness of the fit, based on the Kolmogorov-Smirnov statistics +computed on num_test sampled distributions from the theoretical +power-law function. If num_test is not provided, the test is based +on 100 sampled distributions.

+ +

PARAMETERS

+ +
+
data_in

Set of values to fit. If is equal to - (dash), read the set from + STDIN.

+
tol

The acceptable statistical error on the estimation of the + exponent. If omitted, it is set to 0.1.

+
TEST

If the third parameter is TEST, the program computes an estimate + of the p-value associated to the best-fit, based on num_test + synthetic samples of the same size of the input set.

+
num_test

Number of synthetic samples to use for the estimation of the + p-value of the best fit.

+
+ + +

OUTPUT

+ +

If fitmle is given less than three parameters (i.e., if TEST is +not specified), the output is a line in the format:

+ +
    gamma k_min ks
+
+ +

where gamma is the estimate for the exponent, k_min is the +smallest of the input values for which the power-law behaviour holds, +and ks is the value of the Kolmogorov-Smirnov statistics of the +best-fit.

+ +

If TEST is specified, the output line contains also the estimate of +the p-value of the best fit:

+ +
    gamma k_min ks p-value
+
+ +

where p-value is based on num_test samples (or just 100, if +num_test is not specified) of the same size of the input, obtained +from the theoretical power-law function computed as a best fit.

+ +

EXAMPLES

+ +

Let us assume that the file AS-20010316.net_degs contains the degree +sequence of the data set AS-20010316.net (the graph of the Internet +at the AS level in March 2001). The exponent of the best-fit power-law +distribution can be obtained by using:

+ +
    $ fitmle AS-20010316.net_degs 
+    Using discrete fit
+    2.06165 6 0.031626 0.17
+    $
+
+ +

where 2.06165 is the estimated value of the exponent gamma, 6 is +the minimum degree value for which the power-law behaviour holds, and +0.031626 is the value of the Kolmogorov-Smirnov statistics of the +best-fit. The program is also telling us that it decided to use the +discrete fitting procedure, since all the values in +AS-20010316.net_degs are integers. The latter information is printed +to STDERR.

+ +

It is possible to compute the p-value of the estimate by running:

+ +
    $ fitmle AS-20010316.net_degs 0.1 TEST
+    Using discrete fit
+    2.06165 6 0.031626 0.17
+    $
+
+ +

which provides a p-value equal to 0.17, meaning that 17% of the +synthetic samples showed a value of the KS statistics larger than that +of the best-fit. The estimation of the p-value here is based on 100 +synthetic samples, since num_test was not provided. If we allow a +slightly larger value of the statistical error on the estimate of the +exponent gamma, we obtain different values of gamma and k_min, +and a much higher p-value:

+ +
    $ fitmle AS-20010316.net_degs 0.15 TEST 1000
+    Using discrete fit
+    2.0585 19 0.0253754 0.924
+    $
+
+ +

Notice that in this case, the p-value of the estimate is equal to +0.924, and is based on 1000 synthetic samples.

+ +

SEE ALSO

+ +

deg_seq(1), power_law(1)

+ +

REFERENCES

+ + + + +

AUTHORS

+ +

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

+ + +
    +
  1. www.complex-networks.net
    2. +
  2. September 2017
    3. +
  3. fitmle(1)
    4. +
+ +
+ + -- cgit v1.2.3