1 Erratum to: Stoch Environ Res Risk Assess DOI 10.1007/s00477-008-0249-z

Equations (6), (7), (12), and (13) are incorrect because of a misprint. In these formulas, \( \partial C(u,v)/\partial u \) should be \( \partial^{2} C(u,v)/\partial u\partial v = c(u,v). \) The correct forms of the abovementioned equations are presented as follows:

$$ \left\{ {\begin{aligned}& {E[Y|X = 0] = \frac{p_{01}}{{p_{00} + p_{01} }}\int\limits_{0}^{ + \infty } {yh_{Y} (y)dy} } \hfill \\ &{E[Y|X = x,X > 0] = \frac{{p_{11} f\left( x \right)}}{{p_{10} h_{X} (x) + p_{11} f(x)}}\int\limits_{0}^{1} {G^{ - 1} (v)c(u,v)dv} } \hfill \\ \end{aligned} } \right., $$
(6)
$$ \left\{ {\begin{aligned}& {Var[Y|X = 0] = \frac{{p_{01} }}{{p_{00} + p_{01} }}\int\limits_{0}^{ + \infty } {y^{2} h_{Y} (y)dy - E^{2} [Y|X = 0]} } \hfill \\ &Var[Y|X = x,X > 0] = \frac{{p_{11} f(x)}}{{p_{10} h_{X} (x) + p_{11} f(x)}}\int\limits_{0}^{1} {(G^{ - 1} (v))^{2} c(u,v)dv} \\ &\qquad\qquad \qquad\qquad\quad- E^{2} [Y|X = x,X > 0] \\ \end{aligned} } \right., $$
(7)
$$ \left\{ {\begin{aligned}& {E[Y|X = 0] = \frac{{p_{01} }}{{p_{00} + p_{01} }}\int\limits_{0}^{ + \infty } {y\left[ {(\kappa_{Y} + 1)\nu_{Y} [G(y)]^{{\nu_{Y} - 1}} - \kappa_{Y} } \right]g(y)dy} } \hfill \\ &{E[Y|X = x,X > 0] = \frac{{\kappa_{X} }}{{(\kappa_{X} + 1)\nu_{X} [F(x)]^{{\nu_{X} - 1}} }}\int\limits_{0}^{1} {G^{ - 1} (v)c(u,v)dv} } \hfill \\ \end{aligned} } \right., $$
(12)

and

$$ \left\{ {\begin{aligned} \begin{aligned} Var[Y|X = 0] = & \frac{{p_{01} }}{{p_{00} + p_{01} }}\int\limits_{0}^{ + \infty } {y^{2} \left[ {(\kappa_{Y} + 1)\nu_{Y} [G(y)]^{{\nu_{Y} - 1}} - \kappa_{Y} } \right]g(y)dy} \\ & - E^{2} [Y|X = 0] \\ \end{aligned} \hfill \\ \begin{aligned} Var[Y|X = x,X > 0] = & \frac{{\kappa_{X} }}{{(\kappa_{X} + 1)\nu_{X} [F(x)]^{{\nu_{X} - 1}} }}\int\limits_{0}^{1} {(G^{ - 1} (v))^{2} c(u,v)dv} \\ & - E^{2} [Y|X = x,X > 0] \\ \end{aligned} \hfill \\ \end{aligned} } \right.. $$
(13)

Furthermore, in Eq. (9), F(X) should be F(x).