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Aim Biodiversity loss could reduce primary productivity and the carbon storage provided by forests; however, the mechanisms underpinning the effects of biodiversity on multiple ecosystem functions are not completely understood. Spanish forests are of particular interest because of the broad variation in environmental conditions and management history. We tested for the existence of a relationship between diversity effects and both carbon storage and tree productivity, and examined the relative importance of complementarity and selection mechanisms in a wide variety of forests, from cold deciduous Atlantic to xeric Mediterranean evergreen forests. Location Continental Spain. Methods We used c. 54,000 plots of the Spanish Forest Inventory and maximum likelihood techniques to quantify how climate, stand structure and diversity shape carbon storage and tree productivity. Diversity effects included both complementarity and selection mechanisms, measured respectively through functional diversity and functional identity measures. Results Diversity had a significant effect on both carbon storage and tree productivity, even when controlling for confounding factors of climate and stand structure. A consistent positive effect of functional diversity on carbon storage and tree productivity was observed in all seven forest types studied. This relationship was not linear, and the largest changes in carbon storage and tree productivity were observed at low levels of functional diversity. However, the importance of complementarity effects was not consistent with the productivity of different forest types. Selection effects were particularly important in deciduous and Mediterranean pine forests, but had very little effect on mountain pines. Main conclusions We found a generally positive effect of diversity on carbon storage and tree productivity, supported by both complementarity and selection mechanisms. Thus, both functionally diverse forests and functionally important species should be maintained to adequately preserve and promote key ecosystem functions such as carbon storage and tree productivity.

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.

This paper focuses on the estimation of income distribution from grouped data in the form of quantiles. We propose a novel application of the minimum quantile distance (MQD) approach and compare its performance with the maximum likelihood (ML) technique. The estimation methods are applied using three parametric distributions: the generalized beta distribution of the second kind (GB2), the Dagum distribution, and the Singh–Maddala distribution. We provide the density-quantile functions for these distributions, along with reproducible R code. A simulation study is conducted to evaluate the performance of the MQD and ML methods. The proposed methods are then applied to data from 30 European countries, utilizing the aforementioned parametric distributions. To validate the accuracy of the estimates, we compare them with estimates obtained from more detailed and informative microdata sets. The findings confirm the excellent performance of the considered parametric distributions in estimating income distribution. Additionally, the MQD approach is identified as a straightforward and reliable method for this purpose. Notably, the MQD method displays superior robustness in comparison to the ML technique when it comes to selecting suitable starting values for the underlying computation algorithm, specifically when dealing with the GB2 distribution.

In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets.

In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindley’s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

In this study, a new generalization of Samade distribution has been proposed. The weighted Samade distribution (WSD) is a new distribution designed for modeling real-life data. The survival function, hazard function, moments, moment-generating function, order statistics, and entropies of this distribution have all been determined. The parameters of the suggested model are estimated using the maximum likelihood estimation technique. Finally, the helpfulness and application of the distribution have been demonstrated by lung cancer data.

PurposeThe main aim of this paper is to verify whether the modern mainstream economic theory of multinational enterprise that explains foreign direct investment (FDI) from developed countries is also able to account for investment decisions of multinational enterprises (MNEs) from emerging economies.Design/methodology/approachUsing Knowledge-And-Physical-Capital (KAPC) model as an analytical framework and Poisson-pseudo maximum likelihood estimation technique, the authors identify determinants of FDI flows from emerging economies. The data set consists of 38 home and 134 host countries during the period 2000–2012. Empirical evidence supports high explanatory power of KAPC model. Further, compared with the earlier Knowledge-Capital (KC) model, results confirm the importance of physical capital.FindingsThe estimation results confirm the hypothesis that mainstream economic theory can explain FDI flows from the emerging economies by highlighting the roles of total market size, skilled-labor abundance, investment and trade costs and geographical distance between two countries.Research limitations/implicationsThis study casts doubt on the alternative way that the KAPC model suggests to distinguish between horizontal and vertical FDI. The argument that horizontal MNE headquarters would be relatively more abundant than vertical MNE headquarters in countries that are abundant in physical capital relative to skilled labor seems reasonable but the idea of variable specification in the estimated equation should be revised.Practical implicationsFirms should be allowed to move their resources freely into and out of specific activities, both internally and internationally across border. To reach that goal, governments of potential host countries can adopt several measures, most importantly remove restrictions on payments, transfers and capital transactions and open previously closed industries to welcome foreign investment. In addition, to improve investment climate in general, governments need to pay attention to enhancing security of property rights, regulating internal taxation (i.e. corporate income tax), guaranteeing adequacy of infrastructure, efficient functioning of finance and labor markets and fighting against corruption.Social implicationsThe location choice of emerging investors set priority on similarity in economic size, geographical and cultural proximity. It is because shared borders or common official languages would reduce information costs and enhance information flows. Also, investors consider horizontal FDI (with motivation to expand market demand) as one of main modes of entry into a foreign market and a substitute for export. Likewise, distance is often understood as an important investment friction.Originality/valueThe outstanding contribution is that the research has uncovered the positive and statistically significant effect of physical capital on FDI activity, which has not been discussed in the earlier KC model. However, at the same time, the study casts doubt on the KAPC model's argument that relative abundance in physical capital to skilled labor between two countries determines FDI types and suggests that this argument and its empirical model specification should be carefully reviewed.

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov—Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

This paper is concerned with the problem of top-K ranking from pairwise comparisons. Given a collection of n items and a few pairwise comparisons across them, one wishes to identify the set of K items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model—the Bradley–Terry–Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress toward characterizing the performance (e.g., the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top-K ranking remains unsettled. We demonstrate that under a natural random sampling model, the spectral method alone, or the regularized MLE alone, is minimax optimal in terms of the sample complexity—the number of paired comparisons needed to ensure exact top-K identification, for the fixed dynamic range regime. This is accomplished via optimal control of the entrywise error of the score estimates. We complement our theoretical studies by numerical experiments, confirming that both methods yield low entrywise errors for estimating the underlying scores. Our theory is established via a novel leave-one-out trick, which proves effective for analyzing both iterative and noniterative procedures. Along the way, we derive an elementary eigenvector perturbation bound for probability transition matrices, which parallels the Davis–Kahan sin Θ theorem for symmetric matrices. This also allows us to close the gap between the ℓ2 error upper bound for the spectral method and the minimax lower limit.