A New Class of Compounded Distribution based on Lindley - Binomial and Gamma - Geometric Models

In this paper, a new compounded distribution obtained by combining the Lindley Binomial and Gamma Geometric distributions is proposed. Several important statistical properties of the proposed distribution, including the probability mass function, cumulative distribution function, and moment generating function, are derived. Expressions for the mean and variance are also obtained. Reliability characteristics such as the survival function and hazard rate function are investigated. Parameter estimation is discussed using several classical estimation methods including maximum likelihood estimation, method of moments, least squares estimation, Cramer von Mises estimation, and Anderson Darling estimation. A Monte Carlo simulation study is conducted to examine the performance of the estimators in terms of bias and mean squared error. The results indicate that the proposed distribution provides a flexible model for analyzing count data and reliability phenomena.

This study introduces a new compounded probability distribution constructed by combining the Lindley Binomial and Gamma Geometric distributions. The proposed model expands the flexibility of statistical modeling for count data and reliability-related phenomena. Its theoretical development includes probability functions, moments, and reliability characteristics, while multiple classical estimation techniques are investigated to estimate its parameters. A Monte Carlo simulation evaluates estimator performance using bias and mean squared error, providing insights into the statistical properties and practical applicability of the proposed distribution.

This paper proposes a new compounded distribution based on the Lindley Binomial and Gamma Geometric distributions. Its fundamental statistical properties, including the probability mass function, cumulative distribution function, moment-generating function, mean, and variance, are derived. Reliability measures, particularly the survival function and hazard rate function, are also investigated. Parameter estimation is performed using maximum likelihood, method of moments, least squares, Cramér–von Mises, and Anderson–Darling methods. A Monte Carlo simulation study assesses the estimators through bias and mean squared error. The results indicate that the proposed distribution offers a flexible framework for modeling count data and reliability phenomena.