Many other generalized forms of the Rayleigh distribution have been proposed including Kundu & Raqab’s ‘s generalized Rayleigh , Merovci & Eltabal’s Weibull-Rayleigh , and Ahmad et al.’s transmuted Rayleigh distribution , but Mohammed et. al  proposed adding the Gompertz-G family of distributions to have more flexibility and greater skewness.
The Gompertz-G family of distributions was introduced by Mohammed et al. in a manner similar to others recently developed. The mathematical properties of the new family are available from a linear mixture of exponentiated-G densities and the creators claim two main advantages in these recent methods:
- They create distributions with several known particular cases.
- The added parameters may provide better fits of the generated distributions to data sets and they can have physical interpretations.
Gompertz-Rayleigh Distribution PDF / CDF
The Gompertz-Rayleigh distribution (GomRD) has the probability density function (PDF):
Where x > 0; θ, α, β > 0.
 Mohammed, F. et al. (2020). A study of some properties and goodness-of-fit of a Gompertz-Rayleigh model. Asian journal of probability and statistics, Page 18-31.
 Kundu, D. & Raqab, M. Generalized Rayleigh Distribution: Different methods of estimations. Comp. Stat. & Data Anal. 2005; 49:187-200
 Merovci, F & Eltabal, I. Weibull-Rayleigh distribution: Theory and applications. Appl. Math & Inf. Sci. 2015; 9(5): 1-11.
 Ahmad et al. Transmuted inverse Rayleigh distribution: A generalization of the inverse Rayleigh distribution. Math Theo. & Mod. 2015; 4(7):90-98.
 Mohamed et. al. Gompertz-G family of distributions. November 2016Journal of Statistical Theory and Practice. 11(1)https://www.researchgate.net/publication/311105965_The_Gompertz-G_family_of_distributions