how to draw a line bewteen two points using the exponential distribution?

I have this figure

and I want to draw a line between the head of first bar (at x=-25) and the end of the red curve(at x=0) like this:

I try to draw the line using the exponential distribution

 EEPY=0.019522:-0.00069:0.00172441;
mu=expfit(EEPY);            % n estimate parameters maximum likelihood exponential 
xgride = linspace(-25,0,100);
Ee=exppdf(xgride,mu);
line(xgride,Ee,'color','g')

and I try another way to draw the line

 EEPY=0.019522:-0.00069:0.00172441;
EEPX=-25:1:0
xvaluese=linspace(min(EEPX),max(EEPX));
yvaluese=interp1(EEPX,EEPY,xvaluese,'spline');
plot(xvaluese,yvaluese,'g--')          % this plot a straight line

but I got nothing...

how I could match the two points

[Amr Hashem]

I try also:

 polyfit(x,y,2);

[Amr Hashem]

Any suggestion ...!

Answer 1

[Kelly Kearney]

expdf fits a pdf to a distribution of points... it doesn't define the pdf at given x-coordinates. So in your code, you're fitting an exponential distribution to uniform data (the x-coordinates), which is of course not what you want.

If you just want a curve following the approximate shape of a negative exponential, then I recommend defining the curve explicitly, rather than messing with fitting:

x1 = -25;   % Coordinates of first bar
y1 = 0.015;
x2 = 0;     % Coordinates of red line start
y2 = 0.0025;

dy = y1 - y2;
dx = x2 - x1;
k = 1;
f = @(x) dy.*exp(-k*(x + dx)) + y2;

x = linspace(x1, x2, 50);
y = f(x);

You can adjust the k parameter to get a steeper or shallower drop-off in the curve.

[Amr Hashem]

thanks...

that definitely what I want .