Linear Combination of Order Statistics of Exponentiated Nadarajah–Haghighi Distribution and Their Applications
B. Singh, Izhar Alam, Aafaq A. Rather, Mahfooz Alam
Abstract
Nadarajah and Haghighi [1] introduced the alternative to the gamma, Weibull and exponentiated exponential distribution with zero mode and allows for increasing, decreasing and constant hazard rates as an extension of exponential distribution. Later Lemonte [2] described the three parameters as exponentiated of the distribution of Nadarajah and Haghighi [1] and given the name as exponentiated Nadarajah–Haghighi (ENH) distribution. Lemonte [2] obtained the rational properties and application of the ENH distribution as moments, entropies, maximum likelihood estimation and stress–strength estimation etc. In this paper, we have obtained the exact expression for single and product moments of order statistics arising from ENH distribution. By using these expressions, we have computed the means of order statistics for $$n=1,...,8$$ and for arbitrarily chosen parameter values. Furthermore, the practical application of our findings was well-suited by the linear combination of these order moments as L-moments. Finally, we interpreted the findings and their future work.