The modified Kies-Fréchet distribution: Properties, inference and application

Mashail M. Al Sobhi; Mashail M. Al Sobhi

doi:10.3934/math.2021276

AIMS Mathematics

2021, Volume 6, Issue 5: 4691-4714. doi: 10.3934/math.2021276

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Research article

The modified Kies-Fréchet distribution: Properties, inference and application

Mashail M. Al Sobhi ^,

Department of Mathematics, Umm-Al-Qura University, Makkah 24227, Saudi Arabia

Received: 09 December 2020 Accepted: 02 February 2021 Published: 24 February 2021
MSC : 60E05, 62F10

The present article introduces a new distribution called the modified Kies-Fréchet (MKF) distribution that extends the Fréchet distribution and provides two new sub-models called modified Kies inverse-exponential and modified Kies inverse-Rayleigh distributions. The MKF model can provide left-skewed, symmetrical, right-skewed, J-shaped, and reversed-J shaped densities. The MKF density was expressed as a linear combination of Fréchet densities. We derive some basic mathematical properties of the MKF model. The MKF parameters are estimated using some classical estimation methods called, the maximum likelihood, Anderson-Darling, least-squares, Cramér-von Mises, and weighted least squares. The performances of these estimators were explored by a detailed simulation study. Finally, the flexibility of the MKF model is checked using a real data set, showing that it can provide close fit as compared with other competing models.
- Fréchet distribution,
- modified Kies family,
- Cramér-von Mises estimation,
- generating function
Citation: Mashail M. Al Sobhi. The modified Kies-Fréchet distribution: Properties, inference and application[J]. AIMS Mathematics, 2021, 6(5): 4691-4714. doi: 10.3934/math.2021276

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Abstract

The present article introduces a new distribution called the modified Kies-Fréchet (MKF) distribution that extends the Fréchet distribution and provides two new sub-models called modified Kies inverse-exponential and modified Kies inverse-Rayleigh distributions. The MKF model can provide left-skewed, symmetrical, right-skewed, J-shaped, and reversed-J shaped densities. The MKF density was expressed as a linear combination of Fréchet densities. We derive some basic mathematical properties of the MKF model. The MKF parameters are estimated using some classical estimation methods called, the maximum likelihood, Anderson-Darling, least-squares, Cramér-von Mises, and weighted least squares. The performances of these estimators were explored by a detailed simulation study. Finally, the flexibility of the MKF model is checked using a real data set, showing that it can provide close fit as compared with other competing models.

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