New Transmuted Rayleigh-Weibull Distribution: Structure and Properties

In this research, the new distribution is built depending on the Rayleigh-Weibull distribution, which is called a new transmuted Rayleigh-Weibull distribution (T R W D). The distribution was built by adding the conversion parameter ß, |ß| ≤1, which contributes to an increase in the flexibility of distribution. At first, the probability cumulative function, the probability density function, the hazard function, and the survival function were found by relying on the transformation rules, and the shapes for these main functions will be discussed at (x⇒∞) and (x⇒0). In addition to this, prove the statistical properties of this distribution, which encompass the median, mean, and moments about the origin. Consequently, by studying the moments of the origin, they found the variance and the first moment, skewness, and kurtosis. In addition, a table will be made to show these properties at different parameter values. Also, it will be found to have a characteristic function, a factorial generating function, a mean time to failure, a quantile function, and the median.