CODEWITHSUNDEEP
matlabbenfords-law
user312141
user312141

Reputation: 33

How to implement Benford's law in MATLAB

I want to implement a version of Benford's law (http://en.wikipedia.org/wiki/Benford%27s_law) that basically asks for the first digit of a number to do analysis on the distribution.

1934---> 1
0.04 ---> 4
-56 ---> 5

How do you do this in MATLAB?

Upvotes: 3

Views: 1626

Answers (4)

Amro
Amro

Reputation: 124563

Let me add another string-based solution (vectorized as well):

FirstDigit = @(n) sscanf(num2str(abs(n(:)),'%e'), '%1d', numel(n));

and tested on the cases mentioned here:

>> FirstDigit( [1934 0.04 -56 eps(realmin)] )
ans =
     1
     4
     5
     4

Upvotes: 0

gnovice
gnovice

Reputation: 125874

A few ways you can do this...

  • Using REGEXP:

    wholeNumber = 1934;                      %# Your number
numberString = num2str(wholeNumber,16);  %# Convert to a string
matches = regexp(numberString,'[1-9]','match');  %# Find matches
firstNumber = str2double(matches{1});  %# Convert the first match to a double

  • Using ISMEMBER:

    wholeNumber = 0.04;                      %# Your number
numberString = num2str(wholeNumber,16);  %# Convert to a string
isInSet = ismember(numberString,'123456789');  %# Find numbers that are
                                               %#  between 1 and 9
numberIndex = find(isInSet,1);           %# Get the first number index
firstNumber = str2double(numberString(numberIndex));  %# Convert to a double

EDIT:

Some discussion of this topic has arisen on one of the MathWorks blogs. Some interesting additional solutions are provided there. One issue that was brought up was having vectorized solutions, so here's one vectorized version I came up with:

numberVector = [1934 0.04 -56];
numberStrings = cellstr(num2str(numberVector(:),16));
firstIndices = regexp(numberStrings,'[1-9]','once');
firstNumbers = cellfun(@(s,i) s(i),numberStrings,firstIndices);

Upvotes: 2

yassin
yassin

Reputation: 6707

function res = first_digit(number)
    number = abs(number);
    res = floor(number / (10 ^ floor(log10(number))));
end

It works for all real numbers (see gnovice's comment for an extreme case)

Upvotes: 4

Doresoom
Doresoom

Reputation: 7458

Using log10 and floor built in functions,

floor(x./10.^floor(log10(x)))

returns the first digit of all elements in an array as well.

Upvotes: 1

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