Some Notes for Two Generalized Trigonometric Families of Distributions

Abstract

The paper deals with two general families of cumulative distribution functions based on arctangent function. We provide analysis of the error of the best one-sided Hausdorff approximation for some special cases of these families. We obtain precious estimates for the value of the Hausdorff distance that can be used as an additional criterion in practice. Further, the family of recurrence generated adaptive functions is constructed and investigated. All new results are illustrated with suitable numerical experiments. Simple dynamic software modules show applicability of Hausdorff approximation.

Keywords

• generated family
• trigonometric distribution
• Hausdorff distance
• Heaviside step function
• upper and lower bounds
• recurrent family