On some mixtures of the Kies distribution

Abstract

The purpose of this paper is to explore some mixtures, discrete and continuous, based on the Kies distribution. Some conditions for convergence are established. We study the probabilistic properties of these mixtures. Special attention is taken to the so-called Hausdorff saturation. Several models are examined in detail – bimodal, multimodal, and mixtures based on binomial, geometric, exponential, gamma, and beta distributions. We provide some numerical experiments for real-life tasks – one for the Standard and Poor’s 500 financial index and another for unemployment insurance issues. In addition, we check the consistency of the proposed estimator using generated data of different sizes.