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This study compares two different series systems under various scenarios for which the components are assumed to be heterogeneous and follow Gompertz-G distributions. In the first scheme, the components of the systems are supposed to be independently distributed. In the second, we compared two series systems in the case that the independent components also experience random shocks. In the last scenario, we considered a case where the components of the systems have dependent structure sharing Archimedean copula. However, in all scenarios, the comparisons are performed based on the concepts of usual stochastic, the hazard rate, and the likelihood ratio orders through the majorization of the Gompertz-G parameters. [ABSTRACT FROM AUTHOR]

This study endeavors to compare two parallel systems delineated via exponentiated half logistic-F distributions with both identical (F) and non-identical (F1 and F2) baseline distribution functions. The comparisons are carried out with respect to the usual stochastic order as well as the reversed hazard rate order through the majorized shape parameters of the distributions. [ABSTRACT FROM AUTHOR]

In this paper, the stress–strength reliability of two multicomponent parallel systems with heterogeneous exponentiated half logistic- F components under the same and the different baseline distribution functions are compared. The comparisons are carried out concerning the usual stochastic order and reversed hazard rate order with majorized shape parameters of the distributions. Also, the maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of the stress–strength reliability of the aforementioned multicomponent parallel system are obtained and then compared via Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In the present paper, we propose the new Janardan-Power Series (JPS) class of distributions, which is a result of combining the Janardan distribution of Shanker et.al (2013) with the family of power series distributions. Here, we examine the fundamental attributes of this class of distribution, including the survival, hazard and reverse hazard functions, limiting behavior of the cdf and pdf, quantile function, moments and distribution of order statistics. Moreover, the particular case of the JPS distribution such as the Janardan- Binomial (JB), Janardan-Geometric (JG), Janardan-Poisson (JP) and the Janardan-Logarithmic (JL) distributions, are introduced. In addition, the JP distribution is analyzed in details. Eventually, an example of the proposed class applied on some real data set. [ABSTRACT FROM AUTHOR]

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. Recommendations for Resource Managers: Through this research, two well‐known indices in drought analysis, including copula‐based joint deficit drought index (JDI) and the SPI‐12 were applied and compared for drought assessment in the arid and semi‐arid regions of Iran. Also, the spatial distributions of drought characteristics (severity, duration, and frequency) have been assessed using the Mann–Kendal approach. This conclusion has four implications for resource managers: ●A joint deficit index (JDI) is defined based on copula functions. This approach provides a probability‐based description of the overall drought status.●The JDI is not only able to reflect the beginning and ending times of drought, but also provides the possibility of monthly drought assessment.●Multivariate analysis of drought characteristics (severity, duration, and frequency) provides an accurate understanding of drought status in arid and semi‐arid regions in Iran.●The results of the meteorological drought analysis using JDI show that this method is a useful tool for managers and decision‐makers to assess the drought conditions in arid and semi‐arid regions. [ABSTRACT FROM AUTHOR]