Corrigendum to Mathematical Models of Meal Amount and Timing Variability with Implementation in the Type-1 Diabetes Patient Decision Simulator

Camerlingo N, Vettoretti M, Del Favero S, Facchinetti A, Sparacino G. Mathematical Models of Meal Amount and Timing Variability With Implementation in the Type-1 Diabetes Patient Decision Simulator. [published online ahead of print September 17, 2020]. Diabetes Technol Ther. doi: 10.1177/1932296820952123

The bold entries in Table 1 of this article have been corrected, the article has been updated of this correction.

Table 1.

Candidate PDF Model Equations.

Candidate PDF model	Equation
Gaussian	$F\left(x;\mathrm{\mu },\mathrm{\sigma }\right)=\frac{1}{\mathrm{\sigma }\sqrt{2\mathrm{\pi }}}\exp \left(-\frac{1}{2}{\left(\frac{x-\mathrm{\mu }}{\mathrm{\sigma }}\right)}^2\right)$
Lognormal	$F\left(x;\mathrm{\mu },\mathrm{\sigma }\right)=\frac{\exp \left(-\frac{{\left(\ln x-\mathrm{\mu }\right)}^2}{2{\mathrm{\sigma }}^2}\right)}{x\sqrt{2\mathrm{\pi }}\mathrm{\sigma }}$
Loglogistic	$\mathit{F}\left(\mathit{x};\mathbf{\alpha },\mathbf{\beta }\right)=\frac{\mathbf{1}}{\mathbf{\alpha }}\frac{\mathbf{1}}{\mathit{x}}\frac{\mathbf{exp}\left(\frac{\mathbf{log}\left(\mathit{x}\right)-\mathbf{\beta }}{\mathbf{\alpha }}\right)}{\left(\mathbf{1}+\mathbf{exp}\left({\frac{\mathbf{log}\left(\mathit{x}\right)-\mathbf{\beta }}{\mathbf{\alpha }}}^2\right)\right)}$
Gamma	$\mathit{F}\left(\mathit{x};\mathbf{\alpha },\mathbf{\lambda }\right)=\frac{{\mathit{x}}^{\mathbf{\alpha }-1}{\mathbf{e}}^{-\frac{\mathit{x}}{\mathbf{\lambda }}}}{{\mathbf{\lambda }}^{\mathbf{\alpha }}\mathbf{\Gamma }\left(\mathbf{\alpha }\right)}$
GEV	$F(x;\mathrm{\mu },\mathrm{\sigma },\mathrm{\xi })=\exp {\left\{-{\left[1+\mathrm{\xi }\left(\frac{x-\mathrm{\mu }}{\mathrm{\sigma }}\right)\right]}^{-\frac{1}{\mathrm{\xi }}}\right\}}^2$
t-Student*	$F\left(x;\mathrm{\nu }\right)=\frac{\mathrm{\Gamma }\left(\frac{\mathrm{\nu }+1}{2}\right)}{\sqrt{\mathrm{\nu }\mathrm{\pi }}\mathrm{\Gamma }\left(\frac{\mathrm{\nu }}{2}\right)}{\left(1+\frac{x^2}{\mathrm{\nu }}\right)}^{-\frac{\mathrm{\nu }+1}{2}}$
Exponential	$F(x;\mathrm{\lambda })=\mathrm{\lambda }{e}^{-\mathrm{\lambda }x}$
Inverse Gaussian	$F\left(x;\mathrm{\mu },\mathrm{\lambda }\right)=\sqrt{\frac{\mathrm{\lambda }}{2\mathrm{\pi }{x}^3}}\exp \left[-\frac{\mathrm{\lambda }{\left(x-\mathrm{\mu }\right)}^2}{2{\mathrm{\mu }}^{2}x}\right]$
Logistic	$F\left(x;\mathrm{\mu },s\right)=\frac{\exp \left(-\frac{x-\mathrm{\mu }}{s}\right)}{s{\left(1+\exp \left(-\frac{x-\mathrm{\mu }}{s}\right)\right)}^2}$
Uniform	$F\left(x;a,b\right)=\frac{1}{b-a},fora\le x\le b$

Abbreviations: GEV, generalized-extreme-value; PDF, probability density function.

*

$\mathrm{\Gamma }$ is the gamma function: $\mathrm{\Gamma }\left(\text{x}\right)=\underset{0}{\overset{\infty }{\int }}{t}^{x-1}{e}^{-t}dt$