4 I am improved formatting edited Sep 18 '16 at 22:18 Michael E2 158k1313 gold badges216216 silver badges514514 bronze badges I am a newbie and I'm trying to use MathematicaMathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie$$\sigma$$, i.e. $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$  , or $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve when these expressions for 0;are 0: Solve[score == {0, 0} && σ>0σ > 0, {μ, σ}]  MathematicaMathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something? I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$   $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; Solve[score == {0,0} && σ>0, {μ,σ}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma$$, i.e. $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$, or $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve when these expressions are 0: Solve[score == {0, 0} && σ > 0, {μ, σ}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something? 3 I am improved formatting edit approved Sep 18 '16 at 22:18 LCarvalho 5,92444 gold badges2929 silver badges8787 bronze badges I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$ $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; Solve[score == {0, 0} && \[Sigma] > 0σ>0, {\[Mu]μ, \[Sigma]σ}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$ $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; Solve[score == {0, 0} && \[Sigma] > 0, {\[Mu], \[Sigma]}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$ $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; Solve[score == {0,0} && σ>0, {μ,σ}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something 2 typeset edited Mar 28 '13 at 17:37 zamazalotta 24122 silver badges77 bronze badges I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$ $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; $$\text{Solve}[\text{score}=\{0,0\}\land \sigma >0,\{\mu ,\sigma \}]$$ Mathematica Solve[score == {0, 0} && \[Sigma] > 0, {\[Mu], \[Sigma]}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$ $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; $$\text{Solve}[\text{score}=\{0,0\}\land \sigma >0,\{\mu ,\sigma \}]$$ Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of the log likelihood for both $$\mu$$ and $$\sigma%$$ ie $$\text{score}=\left\{\frac{\partial \text{logL}}{\partial \mu },\frac{\partial \text{logL}}{\partial \sigma }\right\}$$ $$\left\{\sum _{i=1}^n -\frac{\sqrt{\frac{2}{\pi }} e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)},\sum _{i=1}^n \frac{\sqrt{\frac{2}{\pi }} \left(\mu -x_i\right) e^{-\frac{\left(\mu -x_i\right){}^2}{2 \sigma ^2}}}{\sigma ^2 \text{erfc}\left(\frac{\mu -x_i}{\sqrt{2} \sigma }\right)}\right\}$$ The problem is that when I try to solve these expressions for 0; Solve[score == {0, 0} && \[Sigma] > 0, {\[Mu], \[Sigma]}]  Mathematica tells me that it can't solve it (Solve::nsmet: This system cannot be solved with the methods available to Solve). Is this really such a hard problem or am I missing something 1 asked Mar 28 '13 at 17:11 zamazalotta 24122 silver badges77 bronze badges