The Efficiency of Hazard Rate Preservation Method for Generating Discrete Rayleigh–Lindley Distribution

In this study, we introduce two novel discrete counterparts for the Rayleigh–Lindley mixture, constructed through the application of survival and hazard rate preservation techniques. These two-parameter discrete models demonstrate exceptional adaptability across various data types, including skewed,...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 8; p. 1261
Main Author Ahmad, Hanan Haj
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2024
Subjects
Bayesian analysis
Bayesian inference
Comparative analysis
discretization methods
Efficiency
hazard rate
Mathematical models
maximum likelihood
Maximum likelihood estimation
Methods
Model accuracy
Monte Carlo Markov Chain
Numerical analysis
Numerical methods
Parameter estimation
Parameter modification
Performance evaluation
Probability
Random variables
simulation
Simulation methods
Statistical analysis
Statistical inference
Survival
Survival analysis
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Summary:In this study, we introduce two novel discrete counterparts for the Rayleigh–Lindley mixture, constructed through the application of survival and hazard rate preservation techniques. These two-parameter discrete models demonstrate exceptional adaptability across various data types, including skewed, symmetric, and monotonic datasets. Statistical analyses were conducted using maximum likelihood estimation and Bayesian approaches to assess these models. The Bayesian analysis, in particular, was implemented with the squared error and LINEX loss functions, incorporating a modified Lwin Prior distribution for parameter estimation. Through simulation studies and numerical methods, we evaluated the estimators’ performance and compared the effectiveness of the two discrete adaptations of the Rayleigh–Lindley distribution. The simulations reveal that Bayesian methods are especially effective in this setting due to their flexibility and adaptability. They provide more precise and dependable estimates for the discrete Rayleigh–Lindley model, especially when using the hazard rate preservation method. This method is a compelling alternative to the traditional survival discretization approach, showcasing its significant potential in enhancing model accuracy and applicability. Furthermore, two real data sets are analyzed to assess the performance of each analog.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12081261