The Extended Erlang-Truncated Exponential distribution: Properties and application to rainfall data

Abstract The Erlang-Truncated Exponential ETE distribution is modified and the new lifetime distribution is called the Extended Erlang-Truncated Exponential EETE distribution. Some statistical and reliability properties of the new distribution are given and the method of maximum likelihood estimate was proposed for estimating the model parameters. The usefulness and flexibility of the EETE distribution was illustrated with an uncensored data set and its fit was compared with that of the ETE and three other three-parameter distributions. Results based on the minimized log-likelihood (\(−lˆ\)), Akaike information criterion (AIC), Bayesian information criterion (BIC) and the generalized Cramer–von Mises \(W⋆\) statistics shows that the EETE distribution provides a more reasonable fit than the one based on the other competing distributions.