Applied Mathematics & Information Sciences

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This study developed the Nadarajah Haghighi generalised power Weibull (NHGPW) distribution by compounding the Nadarajah Haghighi and the generalised power Weibull distribution. Various statistical properties of this new distribution are derived for the new distribution. Estimators of the parameters of the developed distribution are also derived using the maximum likelihood estimation. The hazard rate function of the NHGPW distribution has been shown to be monotonically increasing, monotonically decreasing, constant, bathtub, upside down bathtub (unimodal), modified bathtub or modified unimodal. Its probability density function also exhibits various shapes such as decreasing-increasing, decreasing, increasing, increasing-decreasing, decreasing-increasing- decreasing, increasing-decreasing-increasing, positively skewed among others. Monte Carlo simulations conducted on the estimators of the NHGPW distribution showed that, the estimators are consistent since the average bias and mean square error approaches zero as the sample size increases. The NHGPW distribution is applied to two real lifetime data and compared with existing lifetime distributions for a system connected in series. The results showed that, the NHGPW distribution provides a better fit to both data sets than the competing distributions.

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