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We describe a procedure to obtain the plasma parameters from the I-V Langmuircurve by using the Druyvesteyn equation. We propose to include two newparameters, $q$ and $r$, to the usual plasma parameters: plasma potential($V_p$), floating potential ($V_f$), electron density ($n$), and electrontemperature ($T$). These new parameters can be particularly useful to representnon-Maxwellian distributions. The procedure is based on the fit of the I-VLangmuir curve with the $q$-Weibull distribution function, and is motivated byrecent works which use the $q$-exponential distribution function derived fromTsallis statistics. We obtain the usual plasma parameters employing threetechniques: the numerical differentiation using Savitzky Golay (SG) filters,the $q$-exponential distribution function, and the $q$-Weibull distributionfunction. We explain the limitations of the $q$-exponential function, where theexperimental data $V>V_p$ needs to be trimmed beforehand, and this results in alower accuracy compared to the numerical differentiation with SG. To overcomethis difficulty, the $q$-Weibull function is introduced as a naturalgeneralization to the $q$-exponential distribution, and it has greaterflexibility in order to represent the concavity change around $V_p$. We applythis procedure to analyze the measurements corresponding to a nitrogen $N_2$cold plasma obtained by using a single Langmuir probe located at differentheights from the cathode. We show that the $q$ parameter has a very stablenumerical value with the height. This work may contribute to clarify someadvantages and limitations of the use of non-extensive statistics in plasmadiagnostics, but the physical interpretation of the non-extensive parameters inplasma physics remains not fully clarified, and requires further research.

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma