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The Slashed Power Half-Normal Distribution with Applications. MATHEMATICS 2022. [DOI: 10.3390/math10091528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
In this paper, an extension of the power half-normal (PHN) distribution is introduced. This new model is built on the application of slash methodology for positive random variables. The result is a distribution with greater kurtosis than the PHN; i.e., its right tail is heavier than the PHN distribution. Its probability density, survival and hazard rate function are studied, and moments, skewness and kurtosis coefficientes are obtained, along with relevant properties of interest in reliability. It is also proven that the new model can be expressed as the scale mixture of a PHN and a uniform distribution. Moreover, the new model holds the PHN distribution as a limit case when the new parameter tends to infinity. The parameters in the model are estimated by the method of moments and maximum likelihood. A simulation study is given to illustrate the good behavior of maximum likelihood estimators. Two real applications to survival and fatigue fracture data are included, in which our proposal outperforms other models.
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Extended Half-Power Exponential Distribution with Applications to COVID-19 Data. MATHEMATICS 2022. [DOI: 10.3390/math10060942] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper, the Extended Half-Power Exponential (EHPE) distribution is built on the basis of the Power Exponential model. The properties of the EHPE model are discussed: the cumulative distribution function, the hazard function, moments, and the skewness and kurtosis coefficients. Estimation is carried out by applying maximum likelihood (ML) methods. A Monte Carlo simulation study is carried out to assess the performance of ML estimates. To illustrate the usefulness and applicability of EHPE distribution, two real applications to COVID-19 data in Chile are discussed.
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Sief M, Liu X, Abd El-Raheem AERM. Inference for a constant-stress model under progressive type-I interval censored data from the generalized half-normal distribution. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1925673] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Mohamed Sief
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China
- Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt
| | - Xinsheng Liu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China
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Lodhi C, Tripathi YM. Inference on a progressive type I interval-censored truncated normal distribution. J Appl Stat 2019; 47:1402-1422. [DOI: 10.1080/02664763.2019.1679096] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Chandrakant Lodhi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, India
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Ahmadi K, Ghafouri S. Reliability estimation in a multicomponent stress–strength model under generalized half-normal distribution based on progressive type-II censoring. J STAT COMPUT SIM 2019. [DOI: 10.1080/00949655.2019.1624750] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Kambiz Ahmadi
- Independent Researcher in Statistics, Birjand, South Khorasan Province, Iran
| | - Somayeh Ghafouri
- Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran
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