# Questions tagged [polygamma]

For questions about, or related to the polygamma function.

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### Numeric approximation for fitting a Gamma Distribution with a single parameter

Given a series of $N$ observations $\left(x_1, \ldots, x_N\right)$ that follow a Gamma distribution with a single parameter, $\text{Gamma}(k, k)$, what is the maximum likelihood estimate of $k$?. ...
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### How can I get the value of k?

I have to get the value of k in this equation: $\frac{(\lambda T)^k [ln(\lambda T)-\psi(k+1)]}{\Gamma(k+1)}=0$, where $\psi$ is the digamma function. Since $\Gamma(k+1)$ is in the denominator and the ...
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### Solve the system of equations in the maximum likelihood estimation of Gamma distribution parameters

I'm trying to calculate the two parameters of the Gamma distribution by solving the system of two equations obtained by differentiating the ...