Copulas are very efficient functions in the field of statistics and specially in statistical inference. They are fundamental tools in the study of dependence structures and deriving their properties. These reasons motivated us to examine and show  various types of copula functions and their families. Also, we separately explain each method that is used to construct each copula in detail with different examples. There are various outcomes that show the copulas and their densities with respect to the joint distribution functions. The aim is to make copulas available to new researchers and readers who are interested in the modern phenomenon of statistical inferences.

The sequence in the upper part of the Balambo Formation is composed mainly of limestone alternating with marly limestones and dark grey shale in the Bosheen section (eastern Sulaymaniyah, northeastern Iraq) and has been studied in terms of its rare earth element (REE) content. The REEs are very low compared to modern marine sediments. They are depletion in LREEs, and enrichment in HREEs and (La/Yb)_N in the studied rocks, indicating that these sediments retained the REEs pattern of marine waters. The negative Ce anomaly reflects direct sedimentation from marine waters under anoxic conditions with the contribution of terrigenous clays. The positive correlation of ∑REEs with Al, Ti, and Y, and the negative correlation of ∑REE

Modeling data acquisition systems (DASs) can support the vehicle industry in the development and design of sophisticated driver assistance systems. Modeling DASs on the basis of multiple criteria is considered as a multicriteria decision-making (MCDM) problem. Although literature reviews have provided models for DASs, the issue of imprecise, unclear, and ambiguous information remains unresolved. Compared with existing MCDM methods, the robustness of the fuzzy decision by opinion score method II (FDOSM II) and fuzzy weighted with zero inconsistency II (FWZIC II) is demonstrated for modeling the DASs. However, these methods are implemented in an intuitionistic fuzzy set environment that restricts the ability of experts to provide mem

The air flow pattern in a co-current pilot plant spray dryer fitted with a rotary disk atomizer was determined experimentally and modelled numerically using Computational Fluid Dynamics (CFD) (ANSYS Fluent ) software. The CFD simulation used a three dimensions system, Reynolds-Average Navier-Stokes equations (RANS), closed via the RNG k −ε turbulence model. Measurements were carried out at a rotation of the atomizer (3000 rpm) and when there is no rotation using a drying air at 25 ^oC and  air velocity at the inlet of  5 m/s without swirl. The air flow pattern was predicted experimentally using cotton tufts and digital anemometer. The CFD simulation predicted a downward central flowing air core surrounded by a slow

The earth-air heat exchanger (EHX) has a promising potential to passively save the energy consumption of traditional air conditioning systems while maintaining a high degree of indoor comfort. The use of EHX systems for air conditioning in commercial and industrial settings offers several environmental benefits and is capable of operating in both standalone and hybrid modes. This study tests the performance and effectiveness of an EHX design in a sandy soil area in Baghdad, Iraq. The area has a climate of the subtropical semi-humid type. Ambient air temperatures and soil temperatures were recorded throughout the months of 2021. During the months of January and June, the temperatures of the inlet and outflow air at varying air veloci

Nitrogen dioxide NO₂ is one of the most dangerous contaminant in the air, its toxic gas that cause disturbing respiratory effects, most of it emitted from industrial sources especially from the stack of power plants and oil refineries. In this study Gaussian equations modelled by Matlab program to state the effect of pollutant NO₂ gas on area around Durra refinery, this program also evaluate some elements such as wind and stability and its effect on stacks height. Data used in this study is the amount of fuel oil and fuel gas burn inside refinery at a year 2017. Hourly April month data chosen as a case study because it’s unsteady month. After evaluate emission rate of the all fuel and calculate exit velocity from

Global oceanic anoxic events (OAEs) are events of immense importance for a variety of reasons. For instance, they are not only behind most if not all of the mass extinctions which took place during the Cenozoic era, but they are the harbinger for the world's best oil source beds, which humanity depends on to satisfy its energy need. In spite of this, there was little effort to document their presence in Iraq, to fill in for the void here, and as a first step, this paper will attempt to establish a cause and effect relationship between OAE 2 and the Gulneri Formation timing of deposition and organic matter richness. This was done by showing the prevalent occurrence of the globally known OAE 2 positive ∂13Corg excursion and the unique ro