Revisiting Structural Breaks in the Terms of Trade of Primary Commodities (1900–2020)—Markov Switching Models and Finite Mixture Distributions

This paper presents an analysis of the long-term dynamics of the terms of trade of primary commodities (TTPC) using an extended data set for the whole period 1900–2020. Following our original contribution, we implement three approaches of time series—the finite mixture of distributions, the Markov finite mixture of distributions, and the Markov regime-switching model. Our results confirm the hypothesis of the existence of a succession of three different dynamic regimes in the TTPC over the 1900–2020 period. It seems that the uncertainty characterising the long-term dynamic analysis of TTPC is better taken into account with a Markov hypothesis in the transition from one regime to another than without this hypothesis. In addition, this hypothesis improves the quality of the time series segmentation into regimes.

Inference on a new distribution under progressive-stress accelerated life tests and progressive type-II censoring based on a series-parallel system

<abstract><p>It is of great importance for physicists and engineers to assess a lifetime distribution of a series-parallel system when its components' lifetimes are subject to a finite mixture of distributions. The present article addresses this problem by introducing a new distribution called "Poisson-geometric-Lomax distribution". Important properties of the proposed distribution are discussed. When the stress is an increasing nonlinear function of time, the progressive-stress model is considered and the inverse power-law model has suggested a relationship between the stress and the scale parameter of the proposed distribution. Based on the progressive type-II censoring with binomial removals, estimation of the included parameters is discussed using maximum likelihood and Bayes methods. An example, based on two real data sets, demonstrates the superiority of the proposed distribution over some other known distributions. To compare the performance of the implemented estimation methods, a simulation study is carried out. Finally, some concluding remarks followed by certain features and motivations to the proposed distribution are presented.</p></abstract>

Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data

The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.

Merging the components of a finite mixture using posterior probabilities

Methods in parametric cluster analysis commonly assume data can be modelled by means of a finite mixture of distributions. However, associating each mixture component to one cluster is frequently misleading because different mixture components can overlap, and then, associated clusters can overlap too suggesting a unique cluster. A number of approaches have already been proposed to construct the clusters by merging components using the posterior probabilities. This article presents a generic approach for building a hierarchy of mixture components that integrates and generalizes some techniques proposed earlier in the literature. Using this proposal, two new techniques based on the log-ratio of posterior probabilities are introduced. Moreover, to decide the final number of clusters, two new methods are presented. Simulated and real datasets are used to illustrate this methodology.