A new six parameters generalized Weibull-Kumaraswamy-{Lomax) Distribution with a Novel Linear Series Expansion of Its Probability Density
Abstract
One method of generalizing a distribution is to add new parameter to the baseline distribution. In this paper the author discusses this methodology to create a new six parameters generalized Weibull-Kumaraswamy-{Lomax) Distribution. The author utilizes the approach of the T-X{Y} family to add new parameters the baseline distribution Kumaraswamy distribution defined on the unit interval with two shape parameters a & b>0. The author used the Lomax distribution with two parameters α & λ>0 , scale and shape parameters respectively, to link the baseline distribution with the generator distribution. The generator distribution is the Weibull distribution with the two parameters, c & γ>0 , shape and scale parameters respectively as will be explained in the paper. The result is a new distribution with six parameters. The author derived the PDF, CDF, and quantile functions. The author used a new technique to expand the pdf in a linear series expansion that is simple and does not require special function. This makes the computational statistics for the raw moments easier and simpler. The author discusses the Shannon entropy and the paper contains figures for the PDF, CDF and the quantile functions.
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BibTeX
@misc{attia2026parameters,
title = {{A new six parameters generalized Weibull-Kumaraswamy-Lomax) Distribution with a Novel Linear Series Expansion of Its Probability Density}},
author = {Iman Mohamed Attia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13316},
eprint = {2609.13316},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13316},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A new six parameters generalized Weibull-Kumaraswamy-{Lomax) Distribution with a Novel Linear Series Expansion of Its Probability Density
AU - Iman Mohamed Attia
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.13316
UR - https://arxiv.org/abs/2609.13316
AB - One method of generalizing a distribution is to add new parameter to the baseline distribution. In this paper the author discusses this methodology to create a new six parameters generalized Weibull-Kumaraswamy-{Lomax) Distribution. The author utilizes the approach of the T-X{Y} family to add new parameters the baseline distribution Kumaraswamy distribution defined on the unit interval with two shape parameters a & b>0. The author used the Lomax distribution with two parameters α & λ>0 , scale and shape parameters respectively, to link the baseline distribution with the generator distribution. The generator distribution is the Weibull distribution with the two parameters, c & γ>0 , shape and scale parameters respectively as will be explained in the paper. The result is a new distribution with six parameters. The author derived the PDF, CDF, and quantile functions. The author used a new technique to expand the pdf in a linear series expansion that is simple and does not require special function. This makes the computational statistics for the raw moments easier and simpler. The author discusses the Shannon entropy and the paper contains figures for the PDF, CDF and the quantile functions.
ER -