The T–R {Y} power series family of probability distributions
Aouf, M., Osatohanmwen, P., Oyegue, F., Ogbonmwan, S. (2020). The T–R {Y} power series family of probability distributions. EKB Journal Management System, 28(1), 1-18. doi: 10.1186/s42787-020-00083-7
M.K. Aouf; Patrick Osatohanmwen; Francis O. Oyegue; Sunday M. Ogbonmwan. "The T–R {Y} power series family of probability distributions". EKB Journal Management System, 28, 1, 2020, 1-18. doi: 10.1186/s42787-020-00083-7
Aouf, M., Osatohanmwen, P., Oyegue, F., Ogbonmwan, S. (2020). 'The T–R {Y} power series family of probability distributions', EKB Journal Management System, 28(1), pp. 1-18. doi: 10.1186/s42787-020-00083-7
Aouf, M., Osatohanmwen, P., Oyegue, F., Ogbonmwan, S. The T–R {Y} power series family of probability distributions. EKB Journal Management System, 2020; 28(1): 1-18. doi: 10.1186/s42787-020-00083-7

The T–R {Y} power series family of probability distributions

Journal of the Egyptian Mathematical Society
Volume 28, Issue 1, June 2020, Page 1-18  XML PDF (784.55 K)
DOI: 10.1186/s42787-020-00083-7
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Authors
M.K. Aouf1; Patrick Osatohanmwen2; Francis O. Oyegue; Sunday M. Ogbonmwan
1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2Department of Statistics, University of Benin, Benin City, Edo State, Nigeria
Abstract
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.

Keywords
T − R{Y} family; Power series family; Continuous distribution; Discrete distribution; Maximum Likelihood estimation
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