A new discrete distribution on integers: Analytical and applied study on stock exchange and flood data

Abstract

This paper is devoted to the properties and applications of a new one-parameter discrete distribution with support on integers. The new distribution represents a discrete analogue of the double Lindley distribution, a symmetric version of the negative binomial distribution and a weighted version of the Inusah-Kozubowski distribution. Some properties of the new distribution are derived, such as log-concavity, mode(s), cumulative density function, quantile function, probability generating function, raw moments, skewness, kurtosis, and order statistics. The parameter of the distribution is estimated by the maximum likelihood method. The usefulness of the new distribution is illustrated by means of two practical datasets with integer values on ℤ, namely stock exchange and flood data.

Subject Classification:

• 60E05
• 62E15

Keywords:

• Distributions on integers
• Discrete skew laplace distributions
• Quantile function
• Moment properties
• Stock price data