Weibull Distribution is one of most important distribution and it is mainly used in reliability and in distribution of life time. The study handled two parameter and three-parameter Weibull Distribution in addition to five –parameter Bi-Weibull distribution. The latter being very new and was not mentioned before in many of the previous references. This distribution depends on both the two parameter and the three –parameter Weibull distributions by using the scale parameter (α) and the shape parameter (b) in the first and adding the location parameter (g)to the second and then joining them together to produce a distribution with five parameters.

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

Weibull Distribution is one of most important distribution and it is mainly used in reliability and in distribution of life time. The study handled two parameter and three-parameter Weibull Distribution in addition to five –parameter Bi-Weibull distribution. The latter being very new and was not mentioned before in many of the previous references. This distribution depends on both the two parameter and the three –parameter Weibull distributions by using the scale parameter (α) and the shape parameter (b) in the first and adding the location parameter (g)to the second and then joining them together to produce a distribution with five parameters.

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Smart cities have recently undergone a fundamental evolution that has greatly increased their potentials. In reality, recent advances in the Internet of Things (IoT) have created new opportunities by solving a number of critical issues that are allowing innovations for smart cities as well as the creation and computerization of cutting-edge services and applications for the many city partners. In order to further the development of smart cities toward compelling sharing and connection, this study will explore the information innovation in smart cities in light of the Internet of Things (IoT) and cloud computing (CC). IoT data is first collected in the context of smart cities. The data that is gathered is uniform. The Internet of Things,

Dandruff and seborrheic dermatitis (SD) are common skin disorders affecting the scalp and extending to other body sites in the case of SD. They are associated with pruritus and scaling, causing an esthetical disturbance in the population affected.   Treatment of such conditions involves using a variety of drugs for long terms, thus optimizing drug formulation is essential to improve therapeutic efficacy and patient compliance. Conventional topical formulations like shampoos and creams have been widely used but their use is associated with disadvantages. To overcome such effects, novel topical nanotechnology-based formulations are currently under investigation. In the following article, we highlight recently published formulatio

The In this experimental study, natural stone powder was utilized to improve a cohesive soil’s compaction and strength properties. According to the significant availability of limestone in the globe, it has been chosen for the purpose of the study, in addition to considering the existing rock industry massive waste. Stone powder was used in percentages of 4, 8, 12, 16% replaced from the soil weight in dry state. Some of cohesive soil’s consistency, shear, and compaction properties were depicted after improvement. The outcomes yielded in significant amendments in the experimented geotechnical properties after stone powder addition considering 60 days curing period. Cohesion and friction angle were notably increased by