How to use original n-th moments formula to calculate mean, skewness and kurtosis in uniform distribution?

I am very new to MATLAB,

here is the original n-th moments formula:

and pdf shows below:

I know mean=0.5 , skewness = 0 and kurtosis=9/5, but face problem to calculate it in MATLAB.

I have tried:

fun = @(x,n) (x-mean(x).^n

q = integral(@(x) fun(x,1),0,1)

but the answer is wrong.

Thank you all anyway!

Answer 1

[Jeff Miller]

I don't think mean(x) gives you what you want inside fun. Try this:

fun = @(x,n) (x-0.5).^n;

[Jing Tang]

Hi,

Thank you for your suggestion. However, there is no difference btw these two.

I am wandering that my intergal process may be wrong.

Thank you again!

[Jeff Miller]

Well, I am not sure what to tell you. I am getting the right answers with these lines.

Notice that your original post is missing a right parenthesis in this line so it would not even run:

fun = @(x,n) (x-mean(x).^n

It should be

fun = @(x,n) (x-mean(x)).^n

Maybe you have that parenthesis in the wrong place?

[Jing Tang]

ummmmm

Do I misunderstand meaning of 'q'?

When I set this formula, I means n=1 , range from 0 to 1.

q = integral(@(x) fun(x,1),0,1)

so, the answer should be 0.5, not -6.9389e-18 (I have already revise the code).

Thank you!

[Jeff Miller]

With n=1, the answer should be zero, not 0.5. With n=1 your function is computing the average of [x - mean(x)]. Some x's are above the mean, some are below, so by definition the function's value must be zero.

[Jing Tang]

I plot my PDF function below:

my calculus sucks:(

my problem is:

this uniform distribution has 2 formula based on value. I don't know how to put 2 formula in one intergal formula.

I think it's quiet simple, but I can't find a solution.