Beta Sarhan–Zaindin modified Weibull distribution

• A new statistical distribution proposed with some statistical properties.
• The distribution with others are fitted to hydrology and meteorology data.
• Hydrologic and meteorological parameters of the data are obtained.
• Numerical and graphs are listed by computer software.

We introduce a new distribution, so-called beta Sarhan–Zaindin modified Weibull (BSZMW) distribution, which extends a number of recent distributions, among which the modified-Weibull, the exponentiated modified-Weibull, beta Weibull and beta linear failure rate distributions. Various structural properties of the distribution are obtained (sometimes in terms of Meijer’s G-function), such as the moments, moment generating function, conditional moments, mean deviations, entropy, order statistics, mean and variance of the (reversed) residual life and maximum likelihood estimators as well as the observed information matrix. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The BSZMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in meteorology. It is shown that, the distribution has a superior performance among the compared distributions as evidenced by some goodness-of-fit tests. As well, some statistical functions associated with these data such as the return level and mean deviation about the return level are obtained.