Evaluating the potential contribution of urban ecosystem service to climate change mitigation

Urban Ecosystems - Promoting urban greenery through tree planting strategies has been considered as a measure to mitigate climate change. While it is essential to understand the temporal dynamics...     

A new four-parameter discrete distribution with bathtub and unimodal failure rate

In this paper, a discrete counterpart of the general class of continuous beta-G distributions is introduced. A discrete analog of the beta generalized exponential distribution of Barreto-Souza et al. [2], as an important special case of the proposed class, is studied. This new distribution contains some previously known discrete distributions as well as two new models. The hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Some distributional and moment properties of the new distribution as well as its order statistics are discussed. Estimation of the parameters is illustrated using the maximum likelihood method and, finally, the model with a real data set is examined.     

Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form

In this article we study two methodologies which identify and specify canonical form VARMA models. The two methodologies are: (1) an extension of the scalar component methodology which specifies canonical VARMA models by identifying scalar components through canonical correlations analysis; and (2) the Echelon form methodology, which specifies canonical VARMA models through the estimation of Kronecker indices. We compare the actual forms and the methodologies on three levels. Firstly, we present a theoretical comparison. Secondly, we present a Monte Carlo simulation study that compares the performances of the two methodologies in identifying some pre-specified data generating processes. Lastly, we compare the out-of-sample forecast performance of the two forms when models are fitted to real macroeconomic data.     

Central Limit Theorem for ISE of Kernel Density Estimators in Censored Dependent Model

In some long-term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the failure times and its kernel estimate f _n is the integrated square error(ISE). In this article, we derive a central limit theorem for the integrated square error of the kernel density estimators under a censored dependent model.     

Nonparametric estimators for quantile density function under length-biased sampling

Abstract

In this article, the strong uniform consistency of two nonparametric estimators for the quantile density function is established under length-biased sampling. The rate of the strong approximation of the resulting processes of these estimators will be presented as well. A Monte Carlo simulation study is carried out to compare the proposed estimators with each other in terms of mean squared errors.     

Multivariate tail conditional expectation for scale mixtures of skew-normal distribution

In practice, a financial or actuarial data set may be a skewed or heavy-tailed and this motivates us to study a class of distribution functions in risk management theory that provide more information about these characteristics resulting in a more accurate risk analysis. In this paper, we consider a multivariate tail conditional expectation (MTCE) for multivariate scale mixtures of skew-normal (SMSN) distributions. This class of distributions contains skewed distributions and some members of this class can be used to analyse heavy-tailed data sets. We also provide a closed form for TCE in a univariate skew-normal distribution framework. Numerical examples are also provided for illustration.     

An extension of parametric ROC analysis for calculating diagnostic accuracy when underlying distributions are mixture of Gaussian

The semiparametric LABROC approach of fitting binormal model for estimating AUC as a global index of accuracy has been justified (except for bimodal forms), while for estimating a local index of accuracy such as TPF, it may lead to a bias in severe departure of data from binormality. We extended parametric ROC analysis for quantitative data when one or both pair members are mixture of Gaussian (MG) in particular for bimodal forms. We analytically showed that AUC and TPF are a mixture of weighting parameters of different components of AUCs and TPFs of a mixture of underlying distributions. In a simulation study of six configurations of MG distributions:{bimodal, normal} and {bimodal, bimodal} pairs, the parameters of MG distributions were estimated using the EM algorithm. The results showed that the estimated AUC from our proposed model was essentially unbiased, and that the bias in the estimated TPF at a clinically relevant range of FPF was roughly 0.01 for a sample size of n=100/100. In practice, with severe departures from binormality, we recommend an extension of the LABROC and software development for future research to allow for each member of the pair of distributions to be a mixture of Gaussian that is a more flexible parametric form.     

Testing goodness-of-fit for some lifetime distributions with conventional Type-I censoring

A goodness-of-fit test procedure is proposed for some lifetime distributions when the available data are subject to Type-I censoring. The proposed method extends the test procedure of Pakyari and Balakrishnan to other lifetime distributions. The extension to Weibull and log-normal models is studied in details. The new test recovers the nominal level of significance and exhibits more power in comparison to the existing tests for several alternative distributions by means of Monte Carlo simulations. Finally, a real dataset is considered for illustrative purposes.