random number generating RANDI with percentage

How to generating random number with percentage:

value = 0 - 14 with 86%

value = 15 - 28 with 14%

with 1000 array

[Torsten]

Is 86% and 14% also a probability (i.e. random numbers between 0 and 14 are generated with probability 0.86 and random numbers between 15 and 28 are generated with probability 0.14) or a fixed percentage ?

Answer 1

[Image Analyst]

If it's not homework, you can try this:

x = [0, 14, 28];
y = [0, .86, 1.0];
plot(x, y, 'b.-', markerSize=30, LineWidth=2)
grid on;
title("Cumulative Distribution Function")

% Get half a million random numbers
n = 500000

n = 500000

r = GetRandom(n);
% Count # less than 14.  Should be 86% of them.
pct14 = sum(r < 14) / n

pct14 = 0.8596

% Count # more than 14.  Should be 14% of them.
pct14 = sum(r > 14) / n

pct14 = 0.1404

% Function to give 86% of numbers in the range of 0-14 and 14% of the
% numbers in the range 14-28.
function r = GetRandom(n)
r = rand(1, n);
if r < 0.86
    r = r / 0.86;
else
    slope = .14 / 14;
    % y - y0 = slope * (x - x0)
    % Find x
    % x = (y - y0) / slope + x0
    % y0 = 0.86.  x0 = 14.
    r = (r - 0.86) / slope + 14;
end
end

Uses the concept of inverse transform sampling.

https://en.wikipedia.org/wiki/Inverse_transform_sampling

If it's your homework you can't turn in my code.

How do I get help on homework questions on MATLAB Answers? - MATLAB Answers - MATLAB Central

[Takim Mustakim]

my MatLab unrecognized function or variable "GetRandom"

[Image Analyst]

@Takim Mustakim it's right there in the code I posted. Did you not click the "Copy" button in the gray-shaded code block? Did you just click and drag over part of the code? THe code was a bit split up because I ran it in the text box so it interspersed results with the code. That's why you should have clicked the "Copy" button. Anyway, here is the code all in one chunk.

x = [0, 14, 28];
y = [0, .86, 1.0];
plot(x, y, 'b.-', markerSize=30, LineWidth=2)
grid on;
title("Cumulative Distribution Function")
% Get half a million random numbers
n = 500000
r = GetRandom(n);
% Count # less than 14.  Should be 86% of them.
pct14 = sum(r < 14) / n
% Count # more than 14.  Should be 14% of them.
pct14 = sum(r > 14) / n

% Function to give 86% of numbers in the range of 0-14 and 14% of the
% numbers in the range 14-28.
function r = GetRandom(n)
r = rand(1, n);
if r < 0.86
    r = r / 0.86;
else
    slope = .14 / 14;
    % y - y0 = slope * (x - x0)
    % Find x
    % x = (y - y0) / slope + x0
    % y0 = 0.86.  x0 = 14.
    r = (r - 0.86) / slope + 14;
end
end

[Torsten]

@Image Analyst

I think you overlooked the "randi" in the title.

Answer 2

[Walter Roberson]

If you have the Statistics Toolbox, use randsample()

If not then:

Find a number, S, such that S*p is an integer for each probability in the vector p. If you have probabilities such as sqrt(2)/2 that are mathematically irrational then you will need to find a good approximation of an integer rather than being exact.

Once you have S, take each element Value(K) and repeat it round(S*p(K)) times, and collect the repeated values in a vector. For example for .86 and .14 you could use S = 50 and repeat the first value 43 times and the second value 7 times.

Now to draw with weights, use randi() on the length of the vector with repetitions, to pick out elements of the vector. The probability that any one (repeated) element will be drawn will be proportional to the number of repetitions divided by the total length of the vector. For example, 43 copies of 0 out of 50 elements gives a 43/50 = 0.86 probability that 0 would be drawn.

Answer 3

[James Tursa]

One way:

n = 1000;
p = 0.86;
r = rand(n,1);
x = r < p;
m = sum(x);
r(x) = randi([0,14],m,1);
r(~x) = randi([15,28],n-m,1);

Or one could re-use the random numbers already in r, but this seems a bit complicated:

n = 1000;
p = 0.86;
r = rand(n,1);
x = r < p;
r(x) = floor(15*r(x));
r(~x) = floor(14*(r(~x)-p)/(1-p)) + 15;