# Can I make a ' y=k*x^n ' distribution by makedist() ?

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Tamura Kentai on 29 Jul 2019
Commented: Tamura Kentai on 30 Jul 2019
Hi, :
Thank you at first.
I hope to have the relation when loglog(x, y) plot , there will be a straight line, I know the math equation 'y=k*x^n' will make it, since ' log10(y) = log10(k) + n*log10(x)'. So that, if given x = 0:1e-3:1, equally spaced steps (linear), then plot the loglog(x,y), the line will be straight with a slope=n, offset=log10(k).
The question is how to use it with griddedInterpolant() & makedist() ?
t=[1:10];
t2=t'*10;
t=t';
f_base=[t,t2];
f_base
Fitp = griddedInterpolant(f_base(:,1),f_base(:,2),'linear','none');
x=f_base(:,1)*1.1;
lin_y=Fitp(x);
pd = makedist('exponential');
exp_y = pdf(pd,x);
plot(x, lin_y);
loglog(x,exp_y);
plot(x,log(exp_y));
I found the most similar is using makedist('exponential') with 'method' = 'exponential', which has the relation y=1/e*exp(1-x), if take log() with both side, log10(y) = log10(1/e) + (1 - x)*log10(e), here the log(y) won't be linear to log(x), it's linear to 'x' only.
So, may I ask, how to have a logarithm to logarithm relations between the griddedInterpolant() points (steps) or makedist() probability density function ?
I need to specify some points for 'bin' search in an array which x value (indexing) is in linear, but the search result (returned 'y' vs. x) I hope it has the log-log relation.
Can you help to give some hint how to do this ?
Thank you very much.
Best regards.
##### 2 CommentsShowHide 1 older comment
Tamura Kentai on 30 Jul 2019
Hi, :
I tried squeeze more points into the indexing array using for loop. Try making it more approx to a straight line in log-log plane.
But no matter whether using griddedInterpolant() or interp1(), I got error message as pasted in the bottom of the code frame.
I'm sorry, I really don't know what's happening. Could you help ?
Thank you very much.
t=[1:10];
g=1e1*t.^5;
t_ex = [];
g_ex = [];
% n: define the numbers of sampling points between two major terminal of trace.
n = 1e1;
for idx = 1:max(size(t)) - 1
t_expnd = logspace( log10( t(idx) ),log10( t(idx+1) ) ,n );
t_ex = [t_ex, t_expnd];
g_expnd = logspace( log10( g(idx) ),log10( g(idx+1) ) ,n );
g_ex = [g_ex, g_expnd];
end
f_base=[t_ex', g_ex'];
x = 1:1e-3:10;
% Fitp = griddedInterpolant(f_base(:,1),f_base(:,2),'linear','none');
% y=Fitp(x);
y = interp1(f_base(:,1),f_base(:,2),x);
% plot(x,y);
plot(log(x),log(y));
% plot(log(t),log(g));
Error using griddedInterpolant
The grid vectors are not strictly monotonic increasing.
Error in interp1 (line 191)
F = griddedInterpolant(X,V,method);
Error in thinking_loglog_interpolate_2 (line 24)
y = interp1(f_base(:,1),f_base(:,2),x);

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