Poisson distribution

Moment-generating function

Statistics

Entropy (arrow of time)

Physics

Statistical physics

Probability distribution

Beta-binomial distribution

Moment (physics)

Lomax distribution

Estimator

Probability mass function

Negative binomial distribution

Applied mathematics

Mathematics

Geometric distribution

Maximum likelihood

Quantum mechanics

Classical mechanics

Principle of maximum entropy

Entropy

In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.

A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications