Sine Odd Perks-G family of Distributions: Properties, Estimation techniques and Applications with Insurance and Failure data.

Abstract

This paper introduces a new trigonometric family of distributions which is named as ``Sine Odd Perks-G family". Few submodels of the family are proposed including one based on the Lomax distribution named ``Sine Odd-Perks Lomax" distribution. We derive its basic statistical properties and illustrate its behavior through density plots showing right skewed, left skewed, n-shape and symmetrical curves and hazard rate plots capturing shapes such as increasing, decreasing, inverted bathtub, sigmoid, and inverted V-shape. Three-dimensional skewness and kurtosis plots are also visualized. The model parameters are estimated using different estimation methods, and the performance of the estimators is evaluated through Monte carlo simulation study. We also examined the utility of the distribution through actuarial data and failure times data.