The copula functions are frequently used by researchers for modeling dependence structure among the correlated attributes in many areas. The copulas are widely used for the analysis of drought frequency, drought characteristics, drought coincidence risk, uncertainty, and drought forecasting. In this research, we have compared two indices of drought assessment, including SPI‐12 and copula‐based joint deficit index (JDI). In this regard, the drought characteristics, including the severity, duration, and drought frequency have been studied in 25 synoptic stations of Iran during the 1968–2014. The results showed that, unlike JDI, the SPI‐12 is not able to estimate the drought peak during the critical and extreme condition. Although JDI has identified a severe and extreme drought during the pervasive drought, the SPI‐12 estimated a normal condition. The results show that JDI accurately estimates the drought frequency, but the SPI‐12 provided an unexpected estimation is some stations. In addition, the MannKendal trend test for drought characteristics represents that JDI accurately estimates the expected trend (an increasing trend) whereas the SPI‐12 exhibits no significant trend in most stations. Finally, JDI provides a comprehensive assessment of drought for decision‐makers and natural managers.

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This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.