Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

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.

In this paper, the reliability and scheduling of maintenance of some medical devices were estimated by one variable, the time variable (failure times) on the assumption that the time variable for all devices has the same distribution as (Weibull distribution.

The method of estimating the distribution parameters for each device was the OLS method.

The main objective of this research is to determine the optimal time for preventive maintenance of medical devices. Two methods were adopted to estimate the optimal time of preventive maintenance. The first method depends on the maintenance schedule by relying on information on the cost of maintenance and the cost of stopping work and acc

The comparison of double informative priors which are assumed for the reliability function of Pareto type I distribution. To estimate the reliability function of Pareto type I distribution by using Bayes estimation, will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of Pareto  type I distribution . Assuming distribution of three double prior’s chi- gamma squared distribution, gamma - erlang distribution, and erlang- exponential distribution as double priors. The results of the derivaties of these estimators under the squared error loss function with two different double priors. Using the simulation technique, to compare the performance for

Facial recognition has been an active field of imaging science. With the recent progresses in computer vision development, it is extensively applied in various areas, especially in law enforcement and security. Human face is a viable biometric that could be effectively used in both identification and verification. Thus far, regardless of a facial model and relevant metrics employed, its main shortcoming is that it requires a facial image, against which comparison is made. Therefore, closed circuit televisions and a facial database are always needed in an operational system. For the last few decades, unfortunately, we have experienced an emergence of asymmetric warfare, where acts of terrorism are often committed in secluded area with no

Hydrogen fuel is a good alternative to fossil fuels. It can be produced using a clean energy without contaminated emissions. This work is concerned with experimental study on hydrogen production via solar energy. Photovoltaic module is used to convert solar radiation to electrical energy. The electrical energy  is used for electrolysis of water into hydrogen and oxygen by using alkaline water electrolyzer with stainless steel electrodes. A MATLAB computer program is developed to solve a four-parameter-model and predict the characteristics of PV module under Baghdad climate conditions. The hydrogen production system is tested at different NaOH mass concentration of (50,100, 200, 300) gram. The maximum hydrogen produc

The nuclear level density parameter  in non Equi-Spacing Model (NON-ESM), Equi-Spacing Model (ESM) and the Backshifted Energy Dependent Fermi Gas model (BSEDFG) was determined for 106 nuclei; the results are tabulated and compared with the experimental works. It was found that there are no recognizable differences between our results and the experimental -values. The calculated level density parameters have been used in computing the state density as a function of the excitation energies for ⁵⁸Fe and ²⁴⁶Cm nuclei. The results are in a good agreement with the experimental results from earlier published work.

The binary cluster model (BCM) and the two-frequency shell model (TFSM) have been used to study the ground state matter densities of neutron-rich ⁶He and ¹¹Li halo nuclei. Calculations show that both models provide a good description on the matter density distribution of above nuclei. The root-mean square (rms) proton, neutron and matter radii of these halo nuclei obtained by TFSM have been successfully obtained. The elastic charge form factors for these halo nuclei are studied through combining the charge density distribution obtained by TFSM with the plane wave Born approximation (PWBA).

Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef

      In the last decade, 3D models gained interest in many applications, such as games, the medical field, and manufacture. It is necessary to protect these models from unauthorized copying, distribution, and editing. Digital watermarking is the best way to solve this problem. This paper introduces a robust watermarking method by embedding the watermark in the low-frequency domain, then selecting the coarsest level for embedding the watermark based on the strength factor. The invisibility of the watermark for the proposed algorithm is tested by using different measurements, such as HD and PSNR. The robustness was tested by using different types of attacks; the correlation coefficient was applied for the evaluati