A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random...

Area of Science:

• Statistics
• Probability Theory
• Survival Analysis

Background:

• Existing survival models often lack theoretical justification or are overly complex.
• There is a need for parsimonious and theoretically sound survival distributions.

Purpose of the Study:

• To develop a novel parsimonious survival model by integrating the Bilal distribution with the Kavya-Manoharan transformation.
• To analyze the theoretical properties, including probability density function (PDF) and hazard rate behavior.
• To practically assess parameter estimation techniques for the proposed model.

Main Methods:

• Development of a new survival model based on the Bilal distribution and Kavya-Manoharan transformation.
• Analytical derivation of single and product moments of order statistics.
• Parameter estimation using Maximum Likelihood (ML) with Simple Random Sampling (SRS) and Ranked Set Sampling (RSS).
• Numerical simulations to compare sampling techniques.

Main Results:

• The proposed Kavya-Manoharan Bilal Distribution offers a parsimonious approach to survival modeling.
• Explicit equations for moments of order statistics were derived.
• Maximum Likelihood estimation was successfully applied using both SRS and RSS.

Conclusions:

• The novel parsimonious survival model provides a theoretically sound and practically applicable alternative.
• The study demonstrates the utility of integrating existing distributions with transformation families.
• Comparative analysis of sampling techniques provides insights for efficient parameter estimation in survival analysis.