α-Power Transformed Transformed Power Function Distribution With Applications

Idika E. Okorie; Johnson Ohakwe; Bright O. Osu; Chris U. Onyemachi

doi:10.1016/j.heliyon.2021.e08047

α-Power Transformed Transformed Power Function Distribution With Applications

Idika E. Okorie, Johnson Ohakwe, Bright O. Osu, Chris U. Onyemachi

Mathematics

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2 Scopus citations

Abstract

By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α-Power Transformed Transformed Power Function (αPTTPF) distribution. Some of the properties of the αPTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates.

Original language	British English
Article number	e08047
Journal	Heliyon
Volume	7
Issue number	9
DOIs	https://doi.org/10.1016/j.heliyon.2021.e08047
State	Published - Sep 2021

Keywords

Data analysis
Estimation
Goodness-of-fit
Power function distribution
Transformation

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10.1016/j.heliyon.2021.e08047

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title = "α-Power Transformed Transformed Power Function Distribution With Applications",

abstract = "By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α-Power Transformed Transformed Power Function (αPTTPF) distribution. Some of the properties of the αPTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates.",

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author = "Okorie, {Idika E.} and Johnson Ohakwe and Osu, {Bright O.} and Onyemachi, {Chris U.}",

note = "Funding Information: The Authors Wish To Thank The Editor And The Two Reviewers For Their Careful Reading And Comments Which Greatly Improved The Paper Publisher Copyright: {\textcopyright} 2021 The Author(s). Published by Elsevier Ltd.",

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T1 - α-Power Transformed Transformed Power Function Distribution With Applications

AU - Okorie, Idika E.

AU - Ohakwe, Johnson

AU - Osu, Bright O.

AU - Onyemachi, Chris U.

N1 - Funding Information: The Authors Wish To Thank The Editor And The Two Reviewers For Their Careful Reading And Comments Which Greatly Improved The Paper Publisher Copyright: © 2021 The Author(s). Published by Elsevier Ltd.

PY - 2021/9

Y1 - 2021/9

N2 - By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α-Power Transformed Transformed Power Function (αPTTPF) distribution. Some of the properties of the αPTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates.

AB - By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α-Power Transformed Transformed Power Function (αPTTPF) distribution. Some of the properties of the αPTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates.

KW - Data analysis

KW - Estimation

KW - Goodness-of-fit

KW - Power function distribution

KW - Transformation

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VL - 7

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JF - Heliyon

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α-Power Transformed Transformed Power Function Distribution With Applications

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Keywords

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