This function computes the probability density of the Gamma Difference distribution (Klar, 2015) given parameters (\(\alpha_1 > 0\), \(\beta_1 > 0\), \(\alpha_2 > 0\), \(\beta_2 > 0\)) computed by pargdd.
$$f(x, x > 0) = c e^{+\beta_2x}\int_{+x}^\infty z^{\alpha_1-1} (z-x)^{\alpha_2 - 1} e^{-(\beta_1+\beta_2)z}\, \mathrm{d}z\mbox{,}$$
and
$$f(x, x < 0) = c e^{-\beta_1x}\int_{-x}^\infty z^{\alpha_2-1} (z+x)^{\alpha_1 - 1} e^{-(\beta_1+\beta_2)z}\, \mathrm{d}z\mbox{,}$$
where \(c\) is defined as
$$c = \frac{\beta_1^{\alpha_1} \beta_2^{\alpha_2}}{\Gamma(\alpha_1) \Gamma(\alpha_2)}\mbox{,}$$
where \(\Gamma(y)\) is the complete gamma function.
pdfgdd(x, para, paracheck=TRUE, silent=TRUE, ...)Probability density (\(f\)) for \(x\).
A real value vector.
The parameters from pargdd or vec2par.
A logical controlling whether the parameters are checked for validity.
The argument of silent for the try() operation wrapped on integrate().
Additional argument to pass.
W.H. Asquith
Klar, B., 2015, A note on gamma difference distributions: Journal of Statistical Computation and Simulation v. 85, no. 18, pp. 1--8, tools:::Rd_expr_doi("10.1080/00949655.2014.996566").
cdfgdd, quagdd, lmomgdd, pargdd