How to sit a fixed value of k with an array of θ values, or a fixed value of θ with an array of k values?

Hi, I am trying to calculate the Weibull Distribution.

this is the question...

The Wiebull distribution can be used in analysing failure rates, wind speed distributions, etc. where the shape factor, k >0, and the scale factor, λ >0, characterise the distribution profile. An example distribution is shown in the figure below. Write a MATLAB script which calculates the Wiebull distribution as it varies with either the scale or shape parameter; i.e. if varying in scale, use a fixed value for the shape parameter and vice versa. Your script should also plot the distribution.

This is the equation that we are supposed to use:

This is a sample input screen

This is what i have done so far however, I am not sure about what to do next?

clc;
clear;

fprintf('Please enter the minimum value, maximum value and increment value for x (where x is the x axis) ... \n\n')
min = input('Minimum x value (>0): ');
max = input('Maximum x value (> min value): ');
inc = input('Step increment for the x axis : ');

if min > max
fprintf('The maximum x value you have entered was smaller than the minimum x value, please enter another one.\n')
end

if min < 0
fprintf('The minimum x value should be greater or equal to 0, please enter another one.\n')
end

if inc > (max-min)
fprintf('please enter another increment value, where inc < (max - min)\n')
end

thanks

Answer 1

[Asvin Kumar]

A simple way of checking whether your conditions are met would be by using the modified code given below:

flag = 0;
while ~flag
    fprintf('Please enter the minimum value, maximum value and increment value for x (where x is the x axis) ... \n\n')
    min = input('Minimum x value (>0): ');
    max = input('Maximum x value (> min value): ');
    inc = input('Step increment for the x axis : ');

    if min > max
        fprintf('The maximum x value you have entered was smaller than the minimum x value, please enter another one.\n')
    elseif min < 0
        fprintf('The minimum x value should be greater or equal to 0, please enter another one.\n')
    elseif inc > (max-min)
        fprintf('please enter another increment value, where inc < (max - min)\n')
    else 
        flag = 1;
    end
end

Another approach to this would be to use assert. Have a look at it's documentation here: https://www.mathworks.com/help/matlab/ref/assert.html

To display a family of Weibull PDFs you can adapt the following code.

x = min:inc:max;

figure
hold on 

A = 5;
for B = 0.1:0.1:2
    y = wblpdf(x,A,B);
    plot(x,y,'DisplayName',strcat("B = ",string(B)));
end
title(strcat("A = ",string(A)))
legend

figure
hold on 

B = 2;
for A = 0.5:0.5:10
    y = wblpdf(x,A,B);
    plot(x,y,'DisplayName',strcat("A = ",string(A)));
end
title(strcat("B = ",string(B)))
legend

You would see the following plots: