A new family of univariate probability distributions called the T − R {Y} power series
family of probability distributions is introduced in this paper by compounding the T
− R {Y} family of distributions and the power series family of discrete distributions. A
treatment of the general mathematical properties of the new family is carried out
and some sub-families of the new family are specified to depict the broadness of the
new family. The maximum likelihood method of parameter estimation is suggested
for the estimation of the parameters of the new family of distributions. A special
member of the new family called the Gumbel–Weibull–{logistic}–Poisson (GUWELOP)
distribution is defined and found to exhibit both unimodal and bimodal shapes. The
GUWELOG distribution is further applied to a real multi-modal data set to buttress its
applicability.