All Figures

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f1.eps}\end{figure}$ Figure 1: Schematic representation of the of the sLDF for three different cases: main sequence only ( top), main sequence plus a constant post main sequence ( middle), and main sequence plus a bumpy post main sequence ( bottom). The position of the mean ( $\mu _1'$ ) and the region corresponding to $\mu _1' \pm 1\sigma$ are explicitly marked.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f2.eps}\end{figure}$ Figure 2: Top: isochrones in the $\ell _{\rm V}$ vs. B-V color-magnitude diagram for three different age values computed by Girardi et al. (2002) based on the evolutionary tracks by Marigo & Girardi (2001). Bottom: same as above, for $\ell _{\rm K}$ .
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In the text

$\begin{figure} \par\includegraphics[width=16.33cm,clip]{3283f3.eps}\end{figure}$ Figure 3: Details of fast evolutionary phases in the V (solid line, left axis) and K (dotted-line, right axis) bands. Bottom panel: complete isochrones. Middle panels: blow-up of the mass axis, showing details of fast evolutionary phases at three different ages. Top panels: same as middle panels, with a more extreme blow up. The isochrone set is the same of Fig. 2.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3283f4.eps}\end{figure}$ Figure 4: Algorithm to obtain an approximate expression for a pLDF based on the Edgeworth's series.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3283f5.eps}\end{figure}$ Figure 5: Top: $\Gamma _1$ and $\Gamma _2$ values for which the Edgeworth's expression truncated to n=2 approximates the pLDF with a 10% accuracy or better (Eq. (51)). Different shades correspond to different ranges in normalized luminosity. Bottom: $\Gamma _1$ and $\Gamma _2$ values for which the pLDF can be approximated by a Gaussian to better than 10%, within different ranges in normalized luminosity.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3283f6.eps}\end{figure}$ Figure 6: Characterization of a pLDF based on Edgeworth's approximation to the second order and a gaussianity tolerance interval of $\pm$ 10%.
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In the text

$\begin{figure*} \par\includegraphics[width=12.9cm,clip]{3283f7.eps}\end{figure*}$ Figure 7: Main parameters of the luminosity function in several photometric bands, obtained from the isochrones by Marigo & Girardi (2001) and adopting the IMF by Salpeter (1955) in the mass range 0.15-120 $M_\odot$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f8.eps}\end{figure}$ Figure 8: Salpeter's IMF (solid line) compared to two examples of distributed IMFs: rectangular (dashed, $\delta =0.5$ ) and Gaussian (dot-dashed, $\sigma =0.5$ ).
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In the text

$\begin{figure} \par\includegraphics[width=7.35cm,clip]{3283f9.eps}\end{figure}$ Figure 9: Monte Carlo simulations of clusters at solar metallicity and 5.5 Ma in the K band for different values of $N_{\rm tot}$ (Cerviño & Valls-Gabaud 2003, shaded histograms), compared to analytical pLDFs obtained convolving $N_{\rm tot}$ times a sLDF made up of three Gaussians (solid line). The vertical scale is logarithmic in the left panels and linear in the right panels. The analytical sLDF has the same mean and variance of the Monte Carlo simulations; the position of the mean is shown by a vertical dashed vertical line.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{3283f10.eps}\end{figure}$ Figure 10: Comparison between the pLDFs obtained through sLDF convolutions (dashed line) and the Edgeworth's approximation (solid line) for clusters with different $N_{\rm tot}$ values.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{3283f11.eps}\end{figure}$ Figure 11: $\Gamma _1$ and $\Gamma _2$ values of the pLDFs obtained through Monte Carlos simulations (black diamonds), sLDF convolutions (empty circles), and the Edgeworth's approximation (empty squares). Larger $\Gamma _1$ and $\Gamma _2$ correspond to lower $N_{\rm tot}$ values.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f12.eps}\end{figure}$ Figure 12: Cumulants of the monochromatic spectral energy distribution for a 1 Ga luminosity function assuming a Salpeter (1955) IMF in the mass range 0.15-120 $M_\odot$ . The figure shows the region around H $\delta$ , which is marked with a solid line. The lines Ca II H + H $\epsilon$ are marked with dashed lines, and the line Ca II K with dotted lines.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{3283f13.eps}\end{figure}$ Figure 13: Luminosity distribution functions in V for clusters with the LMC metallicity, approximated by the Edgeworth's series, for several ages and cluster masses: 10 $^4~M_\odot$ (solid line), 10 $^{4.5}~M_\odot$ (dashed line) and 10 $^5~M_\odot$ (dotted line). The mean values of the pLDFs are marked as vertical lines.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{3283f14.eps}\end{figure}$ Figure 14: Main parameters of the luminosity function for several photometric bands obtained from the isochrones by Marigo & Girardi (2001) (bold lines) and Bertelli et al. (1994); Girardi et al. (2000) (light lines), assuming a Salpeter (1955) IMF in the mass range 0.15-120 $M_\odot$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f1.eps}\end{figure}$	Figure 1: Schematic representation of the of the sLDF for three different cases: main sequence only ( top), main sequence plus a constant post main sequence ( middle), and main sequence plus a bumpy post main sequence ( bottom). The position of the mean ( $\mu _1'$ ) and the region corresponding to $\mu _1' \pm 1\sigma$ are explicitly marked.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f2.eps}\end{figure}$	Figure 2: Top: isochrones in the $\ell _{\rm V}$ vs. B-V color-magnitude diagram for three different age values computed by Girardi et al. (2002) based on the evolutionary tracks by Marigo & Girardi (2001). Bottom: same as above, for $\ell _{\rm K}$ .
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$\begin{figure} \par\includegraphics[width=16.33cm,clip]{3283f3.eps}\end{figure}$	Figure 3: Details of fast evolutionary phases in the V (solid line, left axis) and K (dotted-line, right axis) bands. Bottom panel: complete isochrones. Middle panels: blow-up of the mass axis, showing details of fast evolutionary phases at three different ages. Top panels: same as middle panels, with a more extreme blow up. The isochrone set is the same of Fig. 2.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3283f4.eps}\end{figure}$	Figure 4: Algorithm to obtain an approximate expression for a pLDF based on the Edgeworth's series.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3283f6.eps}\end{figure}$	Figure 6: Characterization of a pLDF based on Edgeworth's approximation to the second order and a gaussianity tolerance interval of $\pm$ 10%.
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$\begin{figure} \par\includegraphics[width=12.9cm,clip]{3283f7.eps}\end{figure}$	Figure 7: Main parameters of the luminosity function in several photometric bands, obtained from the isochrones by Marigo & Girardi (2001) and adopting the IMF by Salpeter (1955) in the mass range 0.15-120 $M_\odot$ .
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f8.eps}\end{figure}$	Figure 8: Salpeter's IMF (solid line) compared to two examples of distributed IMFs: rectangular (dashed, $\delta =0.5$ ) and Gaussian (dot-dashed, $\sigma =0.5$ ).
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$\begin{figure} \par\includegraphics[width=7.4cm,clip]{3283f10.eps}\end{figure}$	Figure 10: Comparison between the pLDFs obtained through sLDF convolutions (dashed line) and the Edgeworth's approximation (solid line) for clusters with different $N_{\rm tot}$ values.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{3283f11.eps}\end{figure}$	Figure 11: $\Gamma _1$ and $\Gamma _2$ values of the pLDFs obtained through Monte Carlos simulations (black diamonds), sLDF convolutions (empty circles), and the Edgeworth's approximation (empty squares). Larger $\Gamma _1$ and $\Gamma _2$ correspond to lower $N_{\rm tot}$ values.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3283f12.eps}\end{figure}$	Figure 12: Cumulants of the monochromatic spectral energy distribution for a 1 Ga luminosity function assuming a Salpeter (1955) IMF in the mass range 0.15-120 $M_\odot$ . The figure shows the region around H $\delta$ , which is marked with a solid line. The lines Ca II H + H $\epsilon$ are marked with dashed lines, and the line Ca II K with dotted lines.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{3283f13.eps}\end{figure}$	Figure 13: Luminosity distribution functions in V for clusters with the LMC metallicity, approximated by the Edgeworth's series, for several ages and cluster masses: 10 $^4~M_\odot$ (solid line), 10 $^{4.5}~M_\odot$ (dashed line) and 10 $^5~M_\odot$ (dotted line). The mean values of the pLDFs are marked as vertical lines.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{3283f14.eps}\end{figure}$	Figure 14: Main parameters of the luminosity function for several photometric bands obtained from the isochrones by Marigo & Girardi (2001) (bold lines) and Bertelli et al. (1994); Girardi et al. (2000) (light lines), assuming a Salpeter (1955) IMF in the mass range 0.15-120 $M_\odot$ .
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