Here is a script that evaluates the density.
Are there restrictions on what the allowed values are for m?
Your formula gives density=∞ at z=0. It gives complex numbers for z<0, for most values of m. That makes me wonder if the formula is really correct.
%SudhirsDensity.m
%WCR 2021-05-07
zmax=1;
re=1;
m=0;
z=(-20:1:20)*zmax/20;
f=zeros(length(z),1);
k=2*beta((m+4)/(2*m+4),0.5)/(pi*(m+2)*re^2);
for i=1:length(z)
f(i)=k*z(i)^(-(m+4)/(m+2));
end
plot(z,f);
xlabel('z');
ylabel('density');
If you want a random sample, then you would need to know the inverse of the distribution function. The you could draw a random number, p, from U[0,1) and then find the inverse from the inverse distribution function. That is the z value corresponding to point p on the distribution. Do that many times. Then you can plot the histogram of the z values you have obtained. But you can't do any of that, because you do not have the inverse distribution function for this density.
