In this paper, we have considered a new contextualization of the Gini index, giving a particular interpretation of inequality. The Gini index is the most widely used measure of inequality in the world, however, this index does not meet some desirable properties of an inequality indicator, even so, as it is a measure adopted by most countries through the years, makes it a valuable statistical input; which requires adjustments that provide information, making the study of inequality more robust by adding different indicators that can account for their economic, political, and social environment. This article provides a variation of the Gini index with the purpose of compare and classify different territories (the States of Mexico, as well as some countries) with similar Gini index. The classification is carried out into groups (called turbines) with either positive equality, negative equality, positive inequality or negative inequality. The main contribution of this paper lies on distinguish territories with similar Gini index but different in how privileges and facilities are distributed into them.

This paper is concerned with statistical inference for both continuous and discrete phasetype distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton-Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton-Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton–Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton–Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

Cloud forest is a sensitive and vulnerable ecosystem that is threatened by human activities as well as climate change. Previous studies have shown how transitional ecosystems such as cloud forests will be the most negatively impacted by the global increase in temperature. Therefore, the niche modeling framework was used in this study to geographically identify the areas with the climatic potential to host the largest number of key tree species in this ecosystem and to propose them as priority conservation areas. A total of 19 species were modeled using the MaxEnt algorithm; binary maps were generated for each species and combined to produce one potential suitability map and identify climatic priority areas. Thus, 7% of the national area of Mexico shows suitability for the cloud forest ecosystem, although it is currently distributed in less than 1% of the country. Finally, potential suitability areas were compared with natural protected areas, current land use and priority conservation areas. We found that of the current suitable area, only 5% coincides with some federal or state protection regime. Natural protected areas have proven to be a mechanism for forest conservation, so we must consider increasing the number and area of those protected areas that favor the conservation of these key cloud forest species.

A Bayesian approach was developed, tested, and applied to model ordinal response data in monotone non-decreasing processes with measurement errors. An inhomogeneous hidden Markov model with continuous state-space was considered to incorporate measurement errors in the categorical response at the same time that the non-decreasing patterns were kept. The computational difficulties were avoided by including latent variables that allowed implementing an efficient Markov chain Monte Carlo method. A simulation-based analysis was carried out to validate the approach, whereas the proposed approach was applied to analyze aortic aneurysm progression data.

In this paper, we present an extension of the model proposed by Lin & Liu that uses the concept of physiological age to model the ageing process by using phase-type distributions to calculate the probability of death. We propose a finite-state Markov jump process to model the hypothetical ageing process in which it is possible the transition rates between non-consecutive physiological ages. Since the Markov process has only a single absorbing state, the death time follows a phase-type distribution. Thus, to build a mortality table the challenge is to estimate this matrix based on the records of the ageing process. Considering the nature of the data, we consider two cases: having continuous time information of the ageing process, and the more interesting and realistic case, having reports of the process just in determined times. If the ageing process is only observed at discrete time points we have a missing data problem, thus, we use a stochastic Expectation–Maximisation (SEM) algorithm to find the maximum likelihood estimator of the intensity matrix. And in order to do that, we build Markov bridges which are sampled using the Bisection method. The theory is illustrated by a simulation study and used to fit real data.

No abstract

No abstract