How can the shape of the following exponential-based curve be controlled, so that the peak value $(Y)$ and the total area under the curve $(E)$ are maintained while increasing the skewness?
$$ y(x)= x \space \exp \left( 1-\frac{Y\exp(1)}{E} \space x \right) \frac{Y}{\delta} $$
Note that in the equation above, the peak value $Y$ occurs at $x=\delta$:
$$y(\delta) = Y, \hspace{10pt}where\hspace{10pt} \delta=\frac{E}{Y\exp(1)} $$
Also, as shown in the figure below for $Y=200$, $E=(20,10)$, as $E$ decreases the peak value shifts further to the left.
I would like to "shift" the peak value to the left, so that $\delta$ becomes small and the curve is positively skewed, while $Y$ and $E$ are held constant. Are there additional parameters that can be added to this equation to accomplish this goal?
