New Lifetime Alpha Power Rayleigh Weibull Distribution: Structure and Properties - Ahmed, Zainab Ali; Mohammed, Ali Talib; Enver, Aytekin (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2025)
Alpha power transformation family distributions (APT) are considered one of the modern transformations that have received the attention of researchers in the past decade and are concerned with adding a shape parameter. Based on APT, this paper proposes a new distribution by adding a new parameter to the two-parameter Rayleigh Weibull distribution, a new continuous distribution called alpha power Rayleigh Weibull distribution (APRWD) including three parameters  where ρ is known as shape parameter and ɑ, δ as scale parameters. This paper also includes a presentation of the mathematical construction of the basic statistical functions: cumulative, probability density, survival, and hazard functions. We also include an expansion of the cumulative and probability density functions to use them in investigating and finding several mathematical statistical properties of (APRWD) such as moments, skewness, Kurtosis, moment generating, characteristics, mode, quantile, and factorial moments generating functions