# Hydrological Drought Frequency Analysis in Water Management Using Univariate Distributions
## 4 Results
The resulting values of the estimated parameters are presented in Table 9, for both estimation methods, for 1-day low flow analysis. For the analysis of deficit volumes and durations of annual droughts, only three distributions of three parameters are presented. The calculations were made only for the estimation of parameters with L-moments, because MOM requires the choice of skewness, there being no criteria for this. The same considerations apply to the statistical analysis of drought durations. The distributions PE3 and W3 were chosen because they best estimate the data set, PE3 being also the parent distribution in Romania. The LN3 distribution is presented comparatively, as it is generally considered an alternative to PE3 [20]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**P**} & \multicolumn{8}{c}{**Probability Distributions**} \\ \cline{2-10}  & **LN3** & **PE3** & **IPV** & **WH3** & **FL3** & **W3** & **WK5** & **L5** \\ \cline{2-10}  & & \multicolumn{8}{c}{**[m3/s]**} \\ \hline
50 & 0.304 & 0.299 & 0.306 & 0.272 & 0.301 & 0.296 & 0.290 & 0.297 \\ \hline
70 & 0.240 & 0.235 & 0.241 & 0.218 & 0.238 & 0.232 & 0.228 & 0.237 \\ \hline
90 & 0.169 & 0.172 & 0.167 & 0.199 & 0.171 & 0.174 & 0.179 & 0.179 \\ \hline
95 & 0.142 & 0.152 & 0.138 & 0.198 & 0.147 & 0.158 & 0.169 & 0.159 \\ \hline
97 & 0.126 & 0.142 & 0.121 & 0.198 & 0.134 & 0.151 & 0.165 & 0.147 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Quantile results with MOM. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**P**} & \multicolumn{8}{c}{**Probability Distributions**} \\ \cline{2-10}  & **LN3** & **PE3** & **IPV** & **WH3** & **FL3** & **W3** & **WK5** & **L5** \\ \cline{2-10}  & & \multicolumn{8}{c}{**[m3/s]**} \\ \hline
50 & 0.290 & 0.287 & 0.291 & 0.279 & 0.284 & 0.287 & 0.287 & 0.286 \\ \hline
70 & 0.234 & 0.228 & 0.236 & 0.215 & 0.230 & 0.227 & 0.227 & 0.227 \\ \hline
90 & 0.180 & 0.180 & 0.180 & 0.186 & 0.185 & 0.180 & 0.180 & 0.181 \\ \hline
95 & 0.163 & 0.169 & 0.160 & 0.184 & 0.172 & 0.169 & 0.170 &Figure 9 shows the frequency curves used for the annual deficit volumes corresponding to the thresholds of 95%, 90% and 80%. Table 10 presents the result values of quantiles for annual deficit volume. Figure 10 shows the frequency curves used for the annual drought durations corresponding to the thresholds of 95%, 90% and 80%. The calculations were made only to estimate the parameters with L-moments. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Distributions**} & \multicolumn{8}{c}{**Probability [\%]**} \\ \cline{2-13}  & **5** & **10** & **20** & **30** & **40** & **50** & **60** & **70** & **80** & **90** \\ \hline \multicolumn{13}{c}{95\% threshold--[1000 m\({}^{3}\)]} \\ \hline LN3 & 193.01 & 154.51 & 106.01 & 66.71 & 23.51 & 0 & 0 & 0 & 0 & 0 \\ \hline PE3 & 196.16 & 154.69 & 106.06 & 66.63 & 23.35 & 0 & 0 & 0 & 0 & 0 \\ \hline W3 & 194.24 & 156.61 & 107.05 & 65.83 & 21.01 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Quantile results for annual deficit volume. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{1}{c}{**LN3**} & **PE3** & **IPV** & **WH3** & **FL3** & **W3** & **WK5** & **L5** & **LN3** & **PE3** & **IPV** & **WH3** & **FL3** & **W3** & **WK5** & **L5** \\ \cline{2-13}  & \multicolumn{8}{c}{**MOM**} & \multicolumn{8}{c}{**L-moments**} \\ \hline \(a\) & \(-1.121\) & 2.024 & 13.0 & 0.129 & 0.482 & 1.26  
Table 11 presents the result values of quantiles for annual drought duration. The performance of the analyzed distribution was evaluated using the relative mean error (RME) and relative absolute error (RAE) criteria [40]. \[RME=\frac{1}{n}\cdot\sqrt{\sum_{i=1}^{n}\left(\frac{x_{i}-x(p)}{x_{i}}\right)^{2}} \tag{96}\]  
\[RAE=\frac{1}{n}\cdot\sum_{i=1}^{n}\left|\frac{x_{i}-x(p)}{x_{i}}\right| \tag{97}\]  
where \(n,x_{i},x(p)\) represent sample size, observed value, and estimated value for a given probability, respectively.