A flexible model for bounded data with bathtub shaped hazard rate function and applications

M. R. Irshad; S. Aswathy; R. Maya; Amer I. Al-Omari; Ghadah Alomani; M. R. Irshad; S. Aswathy; R. Maya; Amer I. Al-Omari; Ghadah Alomani

doi:10.3934/math.20241208

AIMS Mathematics

2024, Volume 9, Issue 9: 24810-24831. doi: 10.3934/math.20241208

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A flexible model for bounded data with bathtub shaped hazard rate function and applications

1.
Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India
2.
Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan
3.
Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 12 June 2024 Revised: 07 August 2024 Accepted: 09 August 2024 Published: 23 August 2024
MSC : 60E05, 60F05

The unit new X-Lindley distribution, which is a novel one-parameter distribution on the unit interval, is presented in this study. It was developed by altering the new X-Lindley distribution using the exponential transformation. This new one-parameter distribution's fundamental features, including moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, mode, extropy, Havrda and Charvat entropy, Rényi entropy, and Tsallis entropy, are explored. Additionally, it has bathtub-shaped hazard rate functions and monotonically increasing hazard rate functions with a single parameter. The new distribution is therefore sufficiently rich to model real data. Also, different estimation methods, such as maximum likelihood, least-squares, and weighted least-squares, are used to estimate the parameters of this model, and using a simulation research, their respective performances are evaluated. Finally, two real-life datasets are used to demonstrate the suggested model's competency.
- new X-Lindley distribution,
- failure time,
- unit new X-Lindley distribution,
- hazard rate function,
- parameter estimation,
- entropy measures,
- empirical studies
Citation: M. R. Irshad, S. Aswathy, R. Maya, Amer I. Al-Omari, Ghadah Alomani. A flexible model for bounded data with bathtub shaped hazard rate function and applications[J]. AIMS Mathematics, 2024, 9(9): 24810-24831. doi: 10.3934/math.20241208

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Abstract

The unit new X-Lindley distribution, which is a novel one-parameter distribution on the unit interval, is presented in this study. It was developed by altering the new X-Lindley distribution using the exponential transformation. This new one-parameter distribution's fundamental features, including moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, mode, extropy, Havrda and Charvat entropy, Rényi entropy, and Tsallis entropy, are explored. Additionally, it has bathtub-shaped hazard rate functions and monotonically increasing hazard rate functions with a single parameter. The new distribution is therefore sufficiently rich to model real data. Also, different estimation methods, such as maximum likelihood, least-squares, and weighted least-squares, are used to estimate the parameters of this model, and using a simulation research, their respective performances are evaluated. Finally, two real-life datasets are used to demonstrate the suggested model's competency.

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