How to make a function that gives probabilities in a Geometric distribution? - matlab

Question

I'm using MATLAB to make a function that returns the probability mass function (PMF) for a Geometric distribution when I enter the values of p, q, and the number of attempts (x) as the inputs.
My function:
function Probability = Geometric(p, q, x)
Probability = p*q^x-1
Now whenever I try to calculate the probability by typing in the values of p, q, and x, such as:
Geometric(0.5, 0.5, 1),
The exact error:
Geometric(0.5,0.5,1)
??? Undefined function or method 'Geometric' for input arguments of type 'double'.
I've tried changing functions, and reducing them to one input and one output.
I expect the probabilities to be calculated, but they just don't.

Answer 1

What's going wrong?
p*q^x-1 % Your original code
Your original code is taking q, raising it the xth power, multiplying it by p, then subtracting 1. This is equivalent to the following code which you certainly didn't intend.
(p*(q^x)) - 1 % What your code was doing written differently
Considering order of operations, the correction is easy.
p*q^(x-1) % Your corrected code
Another possible error source is your function is not saved as a standalone m-file "Geometric.m" which must also be on your MATLAB path (MATLAB has to "see" it). If you have your function file "MyFunction.m" stored in a folder, you can add that folder to MATLAB's visible path with one line (or manually navigate there). For more details, see how to create a function.
mypathtoMyFunction = 'C:\Users\SonnyJordan\Documents\SweetCode\FunctionFolder';
path(path,'mypathtoMyFunction')
A Full Solution (3 approaches)
From your parameterization of the Geometric distribution, you're wanting the support on {1, 2, 3, 4, ...}.
Two things. (1) I'd recommend an anonymous function for something like this. (2) There really isn't a need to separate p and q as separate variables since p + q = 1 and therefore one determines the other (i.e. q = 1-p).
Approach 1: Anonymous function
% MATLAB R2018b
geopmfh =#(p,k) p.*((1-p).^(k-1)); % Define pmf
k = 5; % Number of trials
p = 0.2; % Prob("Success" on trial)
geopmfh(p,k) % Probability
Above code is fully vectorized so you could pass it vectors and/or arrays of inputs.
A quick check to validate it is a valid probability mass function (pmf).
M = 500;
sum(geopmfh(p,[1:M])) % should return 1 if M large enough
Approach 2: Function (w/ error checking)
As an aside, making a function in MATLAB would make a lot of sense if you wanted to add error checking on the function inputs to ensure k is a positive integer and that p is between [0 1].
function [pmf] = geopmf(p,k)
%GEOPMF Calculates pmf for Geometric(p,k) distribution on {1,2,3,...}
% pmf = geopmf(p,k)
% p = n x d matrix of n d-dimensional success probabilities; must be [0,1]
% k = m x d matrix of m d-dimensional numbers of trials
% pmf = n x m matrix of probabilities
%
% Examples:
% k = 4; p = .5;
% pmf = geopmf(p,k) % pmf = 0.0625
% Input Error Checking ****************************************************
if isempty(p) | isempty(k), pmf = []; return, end
if nargin ~= 2, error('Function requires two inputs.'), end
if p < 0 | p > 1, error('p must be between 0 and 1.'), end
if k < 1 | ~isint(k), error('k must be positive integer & k > 0.'), end % with this parameterization
n = size(p,1); d = size(p,2);
m = size(k,1);
if isempty(p) | ~isnumeric(p) | ~ismatrix(p)
error('p must be non-empty numeric scalar, vector, or 2-D matrix.');
elseif isempty(k) | ~isnumeric(k) | ~ismatrix(k)
error('k must be non-empty numeric scalar, vector, or 2-D matrix.');
elseif size(k,2) ~=d
error('Rows of p and k must have same dimensions.');
end
% End (Input Error Checking) **********************************************
pmf = p.*((1-p).^(k-1));
end
Approach 3: MATLAB's built-in function
If you have the Statistics toolbox, MATLAB has a function for this already called geopdf but note it is parameterized according to the other "version" with support {0, 1, 2, ...} (see wiki page).
p.*((1-p).^k) % The other parameterization
geopdf(k,p) % Note order of inputs
You can correct for that by adjusting your input.
geopdf(k-1,p) % Subtract 1 trial
Code tested with MATLAB R2018b.