Determination of the best statistical distribution for low flow analysis

Planning of a water resources scheme, the application of the best operational and managerial practices depends on the knowledge of the magnitudes and the quality of the resources. The future events can be traced by using the appropriate methodology. Among the different methods of prediction of an event the statistical distribution methods are some. The objective of this dissertation is to test and sort out the theoretical distributions that best fit the empirical distribution of the observed data of a hydrometric station. Five candidate distributions were used during the fitness test over 42 hydrometric stations of Tanzania. The candidate distributions used for the test are: (i) Pearson type III distribution (ii) Two parameter lognormal distribution (iii) Three parameter lognormal " (iv) Extreme value type one " (v) Extreme value type three (Weibull) " The method of moments and maximum likelihood procedures were used simultaneously in the parameter estimation. The goodness of fit test was done using the kolmogorov-Smirnov goodness of fit test statistics. Three criteria were set in the determination of the best fit of the theoretical and the observed distributions. These criterion are:- (i) Predictive power of the distribution to give a realistic values at a higher return period. (ii) The performance of a theoretical distribution in minimizing standard error of estimates at higher return periods. (iii) Deserving of an acceptance by the Kolmogorov-Smirnov goodness of fit test.