# Constructing portability density function by convolution of two PDFs and acquire ICDF

I need Gaussian-convoluted gamma distribution to fit my data, but the program I'm using doesn't allow construction of custom PDF. Let's call it pdf_g2.

$$\mathrm{pdf_{g2}}(x,a,b,c,d) = conv[\mathrm{pdf_{gau}}(x,a,b), \mathrm{pdf_{\gamma}}(x,c,d)]$$

My question is that whether the following expression is correct:

$$\int_{-\infty}^{+\infty}dx \ \mathrm{pdf_{g2}}(x) = 1$$

$$\mathrm{icdf_{g2}}(p,a,b,c,d)=conv[\mathrm{icdf_{gau}}(p,a,b), \mathrm{icdf_{\gamma}}(p,c,d)]$$

My end goal is to find the expression of $$\mathrm{icdf_{g2}}(p,a,b,c,d)$$