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Christian Salas-Eljatib

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Coursework


  • Forest biometrics
  • Statistics

A height-diameter model has the following structure \begin{equation} h_i=f({\theta},d_i) + \epsilon_i, \label{eq:modh.0} \end{equation}
where: $h_i$ is height at the $i$-th tree; $d_i$ is diameter at breast height at the $i$-th tree; $f()$ is a mathematical function; ${\theta}$ is a vector of coefficients (i.e., parameters) of model $f()$; $\epsilon_{i}$ is the random term for the $i$-th tree following a Gaussian probability density function having an expected value of zero and variance $\sigma^2_{\epsilon}$. Noice that function $f()$ could either be linear o non-linear.

\begin{tikzpicture}[scale=1.0544]\small \begin{axis}[axis line style=gray, 	samples=120, 	width=9.0cm,height=6.4cm, 	xmin=-1.5, xmax=1.5, 	ymin=0, ymax=1.8, 	restrict y to domain=-0.2:2, 	ytick={1}, 	xtick={-1,1}, 	axis equal, 	axis x line=center, 	axis y line=center, 	xlabel=$x$,ylabel=$y$] \addplot[red,domain=-2:1,semithick]{exp(x)}; \addplot[black]{x+1}; \addplot[] coordinates {(1,1.5)} node{$y=x+1$}; \addplot[red] coordinates {(-1,0.6)} node{$y=e^x$}; \path (axis cs:0,0) node [anchor=north west,yshift=-0.07cm] {0}; \end{axis} \end{tikzpicture}