New hyperbolic sine-generator with an example of Rayleigh distribution: Simulation and data analysis in industry

Abstract

This study focuses on a novel family of distributions inspired by the hyperbolic sine function. The Rayleigh distribution is the base model for the newly formed family of distributions known as the new hyperbolic Sine-Rayleigh distribution. The recommended distribution’s distinct structural traits have been examined. The behaviors of the distributional functions of the proposed model are depicted in several figures. The maximum likelihood estimation procedure is employed to estimate the specified distribution parameters. A simulation study was carried out to examine and evaluate the behavior of the estimators. Moreover, the efficacy of the specified distribution is supported by realistic data sets pertaining to engineering science.

Keywords

• Hyperbolic sine function
• Rayleigh distribution
• Moments
• Ageing indicators
• Simulation
• Maximum likelihood estimation