4 I am improved formatting
source | link

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
source | link

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
source | link

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
source | link