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Table Of Integrals Series And Products

To sustain a clean environment by reducing fossil fuels-based energies and increasing the integration of renewable-based energy sources, i.e., wind and solar power, have become the national policy for many countries. The increasing demand for renewable energy sources, such as wind, has created interest in the economic and technical issues related to the integration into the power grids. Having an intermittent nature and wind generation forecasting is a crucial aspect of ensuring the optimum grid control and design in power plants. Accurate forecasting provides essential information to empower grid operators and system designers in generating an optimal wind power plant, and to balance the power supply and demand. In this paper, we present an extensive review of wind forecasting methods and the artificial neural network (ANN) prolific in this regard. The instrument used to measure wind assimilation is analyzed and discussed, accurately, in studies that were published from May 1st, 2014 to May 1st, 2018. The results of the review demonstrate the increased application of ANN into wind power generation forecasting. Considering the component limitation of other systems, the trend of deploying the ANN and its hybrid systems are more attractive than other individual methods. The review further revealed that high forecasting accuracy could be achieved through proper handling and calibration of the wind-forecasting instrument and method.

https://www.mdpi.com/2071-1050/12/9/3778/pdf

Wind Generation Forecasting Methods and Proliferation of Artificial Neural Network: A Review of Five Years Research Trend

In this paper, a new class of generalized distribution called the Kumaraswamy Power Lindley (KPL) distribution is proposed and studied. This class of distributions contains the Kumaraswamy Lindley (KL), exponentiated power Lindley (EPL), power Lindley (PL), generalized or exponentiated Lindley (GL), and Lindley (L) distributions as special cases. Series expansion of the density is obtained. Statistical properties of this class of distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, quantile function, mean deviations, Bonferroni and Lorenz curves, entropy and Fisher information are derived. Method of maximum likelihood is used to estimate the parameters of this new class of distributions. Finally, a real data example is discussed to illustrate the applicability of this class of distribution.

A New Class of Generalized Power Lindley Distribution with Applications

Purpose – Designing an effective university mobile website is becoming a necessity for universities. With the increasing percentage of students using smart phones to research colleges and universities, many university websites worldwide are moving towards addressing mobile needs. The purpose of this paper is to provide a comprehensive mobile university evaluation framework that can be used to assess how universities' websites respond to the increasing demand for the mobile web, and also to identify trends and gaps in current services provided in universities' mobile websites. Design/methodology/approach – A framework was developed and applied to a set of 35 universities' mobile websites worldwide. The framework consists of four categories: interface, navigation, content and services offered, and technical aspects. Findings – Evaluation findings show that most universities' mobile websites performed well in terms of mobile-friendliness and functionality; however, suggestions for future improvements are giv...

A framework for evaluating university mobile websites

Modeling the diameter distribution of trees in forest stands is a frequent application in ecology that supports key biologically and economically relevant management decisions. The choice of model used to represent the diameter distribution and how to estimate its parameters has received much attention in the forestry literature; however, accessible software that facilitates comprehensive comparison of the myriad modeling approaches is not available. To this end, we developed an R package called ForestFit that simplifies estimation of common probability distributions used to model tree diameter distributions, including the two- and three-parameter Weibull distributions, Johnson’s SB distribution, Birnbaum–Saunders distribution, and finite mixture distributions. Frequentist and Bayesian techniques are provided for individual tree diameter data, as well as grouped data. Additional functionality facilitates fitting curves to height-diameter data. The package also provides a set of functions for computing probability distributions and simulating random realizations from common finite mixture models.

ForestFit: An R package for modeling plant size distributions

Weibull distribution has received a wide range of applications in engineering and science. The utility and usefulness of an estimator is highly subject to the field of practitioner's study. In practice users looking for their desired estimator under different setting of parameters and sample sizes. In this paper we focus on two topics. Firstly, we propose $U$-statistics for the Weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of Weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondary, due to lack of a comprehensive comparison between the Weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. Based on simulations, it turns out that the our proposed $U$-statistics show the best performance in terms of bias for estimating the shape and scale parameters when the sample size is large.

A new estimator for Weibull distribution parameters: Comprehensive comparative study for Weibull Distribution

Let X and Y be positive weakly negatively dependent (WND) random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on $\bar F$(x) = 1−F(x) and $\bar G$(x) = 1−G(x) are provided. Moreover, subexponentiality of XY when X and Y are WND random variables is derived.

/pdf/asymptotic-behavior-of-product-of-two-heavy-tailed-dependent-2bpqfl8pir.pdf

Asymptotic behavior of product of two heavy-tailed dependent random variables

Let { } ;1 j Xj ≥ be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let { } ;1 j j θ ≥ be other sequence of positive random variables independent of { } ;1 j Xj ≥ and [] 1 j Pa b θ ≤≤ = for some 0 ab <≤ < ∞ and for all 1 j ≥ . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy-tailed

/pdf/asymptotic-behavior-of-weighted-sums-of-weakly-negative-44rm6zasrj.pdf

Asymptotic behavior of weighted sums of weakly negative dependent random variables

In this study, we introduce a new model called the Extended Exponentiated PowerLindley distribution which extends the Lindley distribution and has increasing, bathtub andupside down shapes for the hazard rate function. It also includes the power Lindley distributionas a special case. Several statistical properties of the distribution are explored, such as thedensity, hazard rate, survival, quantile functions, and moments. Estimation using the maximumlikelihood method and inference on a random sample from this distribution are investigated. Asimulation study is performed to compare the performance of the di®erent parameter estimatesin terms of bias and mean square error. We apply a real data set to illustrate the applicabilityof the new model. Empirical ¯ndings show that proposed model provides better ¯ts than otherwell-known extensions of Lindley distributions.

https://www.ijmex.com/index.php/ijmex/article/download/755/377

Extended Generalized Lindley distribution: properties and applications

In this paper, a notion of fuzzy copula function is introduced by defining joint distribution function of two fuzzy random variables. Using some lemmas, it is proven that the extended fuzzy copula satisfies many desired properties used for non-fuzzy data. The proposed fuzzy copula is then applied to construct some common non-parametric measures of association between two fuzzy random variables. The proposed methods is then illustrated via some numerical examples.

Vahid Ranjbar

Papers

A new estimator for Weibull distribution parameters: Comprehensive comparative study for Weibull Distribution

Asymptotic behavior of product of two heavy-tailed dependent random variables

Asymptotic behavior of weighted sums of weakly negative dependent random variables

Extended Generalized Lindley distribution: properties and applications

Copula function for fuzzy random variables: applications in measuring association between two fuzzy random variables