Erratum
During the processing of this article [1], the following typographical error occurred on page 3: , ui was incorrectly introduced:
1.
inside the exponent in the definition of S
ij
(t|X
ij
, u
i
) following Eq. 3; this should read:
$$ {S}_{ij}\left(t\left|{X}_{ij},{u}_i\right.\right)= \exp \left\{-{\mathit{\int}}_0^t{h}_{ij}\left(x\left|{X}_{ij}\right.,{u}_i\right)\kern0.1em dx\right\}= \exp \left(-{H}_{\mathrm{o}}(t){u}_i\beta \mathit{\hbox{'}}\kern0.1em {X}_{ij}\right) $$
2.
inside the exponent in Eq. 4; this should read:
$$ {L_m}_{,i}\left(\phi, \theta, \beta \right)={\displaystyle \prod_{j=1}^{n_i}{\mathit{\int}}_0^{\infty}\kern0.5em }{\left[{h}_{\mathrm{o}}\left({t}_{ij}\right){u}_i \exp \left(\beta \mathit{\hbox{'}}\kern0.1em {X}_{ij}\right)\right]}^{\delta_{ij}}\times {S}_{ij}\left({t}_{ij}\left|{X}_{ij},{u}_i\right.\right)\kern0.1em \mathit{\mathsf{g}}\kern0.1em \left({u}_i;\theta \right)d{u}_i $$
3.
Twice in Eq. 5; this should read:
$$ \begin{array}{l}{l}_m\left(\phi, \theta, \beta \right)={\displaystyle \sum_{i=1}^K\kern0.1em \left[ \log \varGamma \left\{\left(1/\theta \right)+{d}_i\right\}+{\displaystyle \sum_{j=1}^{n_i}{\delta}_{ij}}\left(\beta \mathit{\hbox{'}}\kern0.1em {X}_{ij}+ \log \left(\upgamma {t}_{ij}^{\upgamma -1}/{\alpha}^{\upgamma}\right)\right)- \log \varGamma \left(1/\theta \right)\right.}\\ {}\left.+{d}_i \log \theta -\left\{\left(1/\theta \right)+{d}_i\right\}\times \log \kern0.5em \left(1+\theta {\displaystyle \sum_{j=1}^{n_i}{\left({t}_{ij}/\alpha \right)}^{\upgamma}} \exp \left(\beta \mathit{\hbox{'}}\kern0.1em {X}_{ij}\right)\right)\right]\end{array} $$
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