We discuss the best methods available for computing gamma function Γ(z) in arbitrary-precision arithmetic with rigorous error bounds. address different cases: rational, algebraic, real or complex arguments; large small low high precision; without precomputation. The also cover log-gamma log Γ(z), digamma ψ(z), and derivatives Γ⁽ⁿ⁾(z) ψ⁽ⁿ⁾(z). Besides attempting to summarize existing state of ar...

Margin maximizing properties play an important role in the analysis of classi£cation models, such as boosting and support vector machines. Margin maximization is theoretically interesting because it facilitates generalization error analysis, and practically interesting because it presents a clear geometric interpretation of the models being built. We formulate and prove a suf£cient condition fo...

Estimation of the mean of the lognormal distribution has received much attention in the literature beginning with Finney (1941). The problem is of significant practical importance because of the ubiquitous use of log-transformation. In this paper we consider estimation of a parametric function associated with the lognormal distribution of which the mean, median and moments are special cases. We...

in this study, the incomplete gamma function, an exponential function, a mixed-log function and a polynomial function were evaluated to describe the lactation curve in moroccan holstein-friesian dairy cows. data from 1990 to 1999, comprising 77130 monthly milk yields of 6029 dairy cows in 280 dairy herds, were used. edits were carried out by considering the lactation length (5 d and

This paper focuses on ozone prediction in the atmosphere using a machine learning approach. We utilize air pollutant and meteorological variable datasets from El Paso area to classify levels as high or low. The LR ANN algorithms are employed train datasets. models demonstrate remarkably classification accuracy of 89.3% predicting given day. Evaluation metrics reveal that both exhibit accuracies...

We introduce a neural network model for regression in which prediction uncertainty is quantified by Gaussian random fuzzy numbers (GRFNs), newly introduced family of subsets the real line that generalizes both variables and possibility distributions. The output GRFN constructed combining GRFNs induced prototypes using combination operator Dempster's rule Evidence Theory. three units indicate mo...

Building off of our interpretations of supervised learning as (1) choosing a representation for our problem, (2) choosing a loss function, and (3) minimizing the loss, let us consider a slightly more general formulation for supervised learning. In the supervised learning settings we have considered thus far, we have input data x ∈ R and targets y from a space Y . In linear regression, this corr...

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the 0-1 loss function. Unlike most of the previous formulations, which rely on surrogate convex loss functions (e.g., hinge-loss in support vector machines (SVMs) and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural 0-1 loss functio...

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the zero-one loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural zero-one loss function. The proposed algorithm ...

The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length ε: roughness (m), ϑ: kinematic viscosity (m2/s), and Ʃk: sum of minor loss coefficients (dimensionless). After applying energy for a hydraulic system composed two tanks connected to constant accepting Colebrook-White Darcy-W...