Decreasing Trend Bumped Probability Distribution: its Properties, Simulations and Application

Abstract

In this paper, a probability model is proposed which engaged the mathematical combination of Lindley distribution and a trigonometric component known as haversine function〖 δ〗_s. The one parameter model prototype sustains the capacity to forecast multimodal decreasing trend sinusoidal outcomes. By nomenclature, the proposed probability model is called Modified Lindley Trigonometric Distribution (MLTD). Some statistical properties studied include the hazard function, mean residual life function, moments, conditional moments and moment generating function, Bonferroni and Lorenz curve, entropy, asymptotic distribution, order statistics, and parameter estimation; where the hazard function specially features a cyclic or periodic bathtub and inverted bathtub shape in chain format. The numerical behavior of the estimates of the average bias and mean square error were examined under Monte Carlo simulation approach; and an applicative simulation is experimented to underscore the parametric behavior of MLTD in data modeling. A real life flood data is used to illustrate the essence of the development.