In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various discip...In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 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 w<sub>i</sub> ∈ 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.展开更多
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 deduc...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.展开更多
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 i...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.展开更多
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 asymptomatica...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.展开更多
文摘In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 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 w<sub>i</sub> ∈ 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.
文摘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.
文摘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.
基金The authors are supported in part by NSERC Discovery GrantsJA is also supported by CIHR through the Canadian 2019 Novel Coronavirus(COVID-19)Rapid Research Funding Opportunity+1 种基金The authors wish to thank Dr.Nicholas Ogden,Director of Public Health Risk Science(PHRS)at the National Microbiology Laboratory of the Public Health Agency of Canada,as well as DrsAamir Fazil and Erin Rees,also with PHRS,for helpful discussions during work on COVID-19.
文摘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.
