The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

Uniformly Minimum-Variance Unbiased Estimator (UMVUE) for the Gamma Cumulative Distribution Function with Known and Integer Scale Parameter

Uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameter. This paper applies Rao-Blackwell and Lehmann-Scheffeé Theorems to deduce the uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameters. The paper closes with an example comparing the empirical distribution function with the UMVUE estimates.

Erlang mixture distribution with application on COVID-19 cases in Egypt

In this paper,a finite mixture of m-Brlang distributions is proposed.Different moments,shape characteristics and parameter estimates of the proposed model are also provided.The proposed mixture has the property that it has a bounded hazard function.A special case of the mixed Erlang distribution is introduced and discussed.In addition,a pre­dictive technique is introduced to estimate the needed number of mixture components to fit a certain data.A real data concerning the confirmed COVID-19 cases in Egypt is introduced to utilize the predictive estimation technique.Two more real datasets are used to examine the flexibility of the proposed model.

Application of Norms Models with Vectoral System in Construction Projects

Normization, i.e., the system of norms is a structure that defines the group of elements containing the norm values for the requirements of a certain resource. Resources comprise of materials, machines and labor. All the requirements of the measure units of the resources are given statically and with the discrete data. Thus, every slight change in the expense list item reference causes a change in norm and our norm is not flexible and features a discrepancy with the real life situations. In order to achieve a higher level of preciseness and to speed up the technological processes of planning and norming the engines of a company that lead to the regulation of the system, the discrete elements of the working （time-related） norms should be replaced by the dynamic ones. This is made possible through setting up norms models that in turn can be presented by formulae in the vectoral system. The use and implementation of the new technologies in terms of production, computer science and cybernetics provides for upgrading the norm requirements. New working tasks in turn require a new norm standardization, which can be applied to the hydrodemolition of concrete constructions by means of water robots that use high pressure water jets.

A simple model for COVID-19

An SL1L2I1I2A1A2R epidemic model is formulated that describes the spread of an epidemic in a population.The model incorporates an Erlang distribution of times of sojourn in incubating,symptomatically and asymptomatically infectious compartments.Basic properties of the model are explored,with focus on properties important in the context of current COVID-19 pandemic.