Sine generalized family of distributions: Properties, estimation, simulations and applications

Abstract

Recent studies have discussed the application and relevance of trigonometry in probability distributions. In this paper, a new, trigonometric family of distributions derived from the alliance of the families known as Sine-G and Generalized G family, inspiring the name Sine Generalized-G Family is proposed and studied. The characteristics of the distribution are explained through the mode, stochastic ordering, quantile function, expansion of the distributional function, and moment. A sub-model of the family named Sine generalized Inverse Gompertz (SG-IG) distribution was studied, its parameters estimated using non-Bayesian and Bayesian procedures. Rigorous simulation studies involving the utilization of the Metropolis–Hasting (MH) algorithm in the Monte Carlo Markov Chain (MCMC) algorithm was carried out to determine the efficiency of the methods and the usefulness was illustrated using two real datasets. The method of Weighted Least squares (WLS) was found to be more efficient in the estimation of parameters of the SG-IG distribution using the lifetime data compared to its competitors.

Keywords

• Sine-G family
• Generalized-G family
• Sine generalized inverted Gompertz distribution
• Maximum likelihood
• Moments
• Real-life data