المتغير العشوائي X  له توزيع أسي اذا كان له دالة احتمالية الكثافة بالشكل:

عندما  ، هذه هي الحالة الخاصة لتوزيع كاما.

غالباً جداً ولسبب معقول تأخذ . الحالة الخاصة لـ (1) التي نحصل عليها تسمى بالتوزيع الاسي لمعلمة واحدة.

اذا كانت  ، ، التوزيع في هذه الحالة يسمى التوزيع الاسي القياسي

اما بالنسب

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

A Geographic Information System (GIS) is a computerized database management system for accumulating, storage, retrieval, analysis, and display spatial data. In general, GIS contains two broad categories of information, geo-referenced spatial data and attribute data. Geo-referenced spatial data define objects that have an orientation and relationship in two or three-dimensional space, while attribute data is qualitative data that can be counted for recording and analysis. The main aim of this research is to reveal the role of GIS technology in the enhancement of bridge maintenance management system components such as the output results, and make it more interpretable through dynamic colour coding and more sophisticated visualization

The research utilizes data produced by the Local Urban Management Directorate in Najaf and the imagery data from the Landsat 9 satellite, after being processed by the GIS tool. The research follows a descriptive and analytical approach; we integrated the Markov chain analysis and the cellular automation approach to predict transformations in city structure as a result of changes in land utilization. The research also aims to identify approaches to detect post-classification transformations in order to determine changes in land utilization. To predict the future land utilization in the city of Kufa, and to evaluate data accuracy, we used the Kappa Indicator to determine the potential applicability of the probability matrix that resulted from

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival

The subject of an valuation of quality of construction projects is one of the topics which it becomes necessary of the absence of the quantity standards in measuring the control works and the quality valuation standards in constructional projects. In the time being it depends on the experience of the workers which leads to an apparent differences in the valuation.

The idea of this research came to put the standards to evaluate the quality of the projects in a special system depending on quantity scale nor quality specifying in order to prepare an expert system “ Crystal “ to apply this special system to able the engineers to valuate the quality of their projects easily and in more accurate ways.

In this work a model of a source generating truly random quadrature phase shift keying (QPSK) signal constellation required for quantum key distribution (QKD) system based on BB84 protocol using phase coding is implemented by using the software package OPTISYSTEM9. The randomness of the sequence generated is achieved by building an optical setup based on a weak laser source, beam splitters and single-photon avalanche photodiodes operating in Geiger mode. The random string obtained from the optical setup is used to generate the quadrature phase shift keying signal constellation required for phase coding in quantum key distribution system based on BB84 protocol with a bit rate of 2GHz/s.

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of B

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est