New lifetime Shanker Weibull distribution: Structure and Properties - Mohammed, Maysaa Jalil; Ashoor, Noor Ebadi; Madaki, Umar Yusuf (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2025)
This paper introduces a new model with two parameters titled “Shanker Weibull distribution". This distribution is obtained by merging the Shanker distribution with a scale of one parameter and the Weibull distribution with a shape parameter. First, we present the mathematical structure of the new distribution, which depends on the survival function for each of the Shanker and Weibull distributions. The statistical functions of this new distribution are presented, such as the cumulative, probability density, hazard and survival functions. In addition, we discuss the behavior of the probability density function and the hazard function by mxamining their shape. We also present the statistical properties of this distribution, which include mode, median and moments around the origin. As a result of studying the moments around the origin, we obtain the variance and the first expected value (mean), the moment generating function, the skewness, the kurtosis, the characteristic function, the factorial generating function, the quantile function and the mean time to failure.