The Novel Bivariate Distribution: Statistical Properties and Real Data Applications

This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.

Bivariate Compound Exponentiated Survival Function of the Lomax Distribution: Estimation and Prediction

In this paper, bivariate compound exponentiated survival function of the Lomax distribution is constructed based on the technique considered by AL-Hussaini (2011). Some properties of the distribution are derived. Maximum likelihood estimation and prediction of the future observations are considered. Also, Bayesian estimation and prediction are studied under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a real data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

Identification of the Mathematical Model of a Gas Turbine Engine Taking Into Account the Uncertainty of the Initial Data

The article describes the method developed by the authors and tested on the example of the AI-25 engine. The study was focused on determining the probability distribution of the output parameters of a gas turbine engine mathematical model. The distribution was obtained considering the uncertainty of the initial data. The paper describes the identified problems and possible ways to solve them. In particular, it was found that it is not possible to study the influence of more than 7..8 input parameters on the probability distribution of output parameters with the current level of development of computer technology even using simple mathematical models. For this reason, a method has been developed to obtain reliable results while reducing the number of considered input data based on sensitivity analysis. The paper also proposed a way of comparing stochastic experimental and computational data with each other using a bivariate distribution. This method allows a precise characterisation of the calculation error using 4 numerical values. The experience obtained in the work has shown that taking into account the uncertainty of the initial data dramatically changes the process of interpreting the results. It should be noted that the obtained results are universal and can be used with other mathematical models in various industries although they were developed on the example of the mathematical model of a gas turbine engine.

Univariate and bivariate extensions of the generalized exponential distributions

The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

Estimation of COVID-19 recovery and decease periods in Canada using delay model

We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. This is possible thanks to some optimization algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. In this purpose, we separate (1) the total cases into 14 groups corresponding to 14 incubation periods, (2) the recovered cases into 406 groups corresponding to a combination of incubation and recovery periods, and (3) the death toll into 406 groups corresponding to a combination of incubation and decease periods. In this paper, we focus on recovery and decease periods and their correlation with the incubation period. The estimated mean recovery period we obtain is 22.14 days (95% Confidence Interval (CI) 22.00–22.27), and the 90th percentile is 28.91 days (95% CI 28.71–29.13), which is in agreement with statistical supported studies. The bimodal gamma distribution reveals that there are two groups of recovered individuals with a short recovery period, mean 21.02 days (95% CI 20.92–21.12), and a long recovery period, mean 38.88 days (95% CI 38.61–39.15). Our study shows that the characteristic of the decease period and the recovery period are alike. From the bivariate analysis, we observe a high probability domain for recovered individuals with respect to incubation and recovery periods. A similar domain is obtained for deaths analyzing bivariate distribution of incubation and decease periods.

Probing electrically driven nanojets by energy and mass analysis in vacuo

Time of flight (TOF) and energy analysis in vacuum are used in series to determine jet velocity Uj, diameter dj, electrical potential Vj and energy dissipated ΔV at the breakup point of electrified nanojets of the ionic liquid 1-Ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (EMI-FAP) (Ignat'ev et al., J. Fluorine Chem., vol. 126, issue 8, 2008, pp.1150–1159). The full spray is periodically gated by a grid held at a high voltage Vg, and received at a collector where the measured flight times provide the distribution of drop speeds u. Varying Vg provides the bivariate distribution of drop energies ξ and velocities. The collector plate, centred with the beam axis, is divided into eight concentric rings, yielding the angular distribution of the spray current, and high resolution (u,ξ) values in the whole spray. The energies of various particles of given u are all well defined, but depend uniquely on u, even though u and ξ are in principle independent experimental variables. Slow and fast particles have energies respectively well above and below the capillary voltage Ve (1.64 kV). As previously shown by Gamero-Castaño & Hruby (J. Fluid Mech., vol. 459, 2002, pp. 245–276), this behaviour is due to the 2-stage acceleration process, first jointly in the jet for all particles, and then separately for free flying drops or ions of different mass/charge. The measured two-dimensional distributions of u and ξ provide the jet velocity Uj (~0.44 km s−1) and electrical potential Vj (1.2 kV) at the breakup point. All molecular ions originate near the breakup point rather than the meniscus neck. A measurable fraction of anomalously fast drops is observed that must come from Coulomb fissions of the main drops.

Estimation of COVID-19 Recovery and Decease Periods in Canada Using Machine Learning Algorithms

We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. This is possible thanks to machine learning algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. In this purpose, we separate i) the total cases into 14 groups corresponding to 14 incubation periods, ii) the recovered cases into 406 groups corresponding to a combination of incubation and recovery periods, and iii) the death toll into 406 groups corresponding to a combination of incubation and decease periods. In this paper, we focus on recovery and decease periods and their correlation with the incubation period. The estimated mean recovery period we obtain is 22.14 days (95% Confidence Interval(CI): 22.00 to 22.27), and the 90th percentile is 28.91 days (95% CI: 28.71 to 29.13), which is in agreement with statistical supported studies. The bimodal gamma distribution reveals that there are two groups of recovered individuals with a short recovery period, mean 21.02 days (95% CI: 20.92 to 21.12), and a long recovery period, mean 38.88 days (95% CI 38.61 to 39.15). Our study shows that the characteristic of the decease period and the recovery period are alike. From the bivariate analysis, we observe a high probability domain for recovered individuals with respect to incubation and recovery periods. A similar domain is obtained for deaths analyzing bivariate distribution of incubation and decease periods.

Estimation of COVID-19 recovery and decease periods in Canada using machine learning algorithms

We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. This is possible thanks to machine learning algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. In this purpose, we separate i) the total cases into 14 groups corresponding to 14 incubation periods, ii) the recovered cases into 406 groups corresponding to a combination of incubation and recovery periods, and iii) the death toll into 406 groups corresponding to a combination of incubation and decease periods. In this paper, we focus on recovery and decease periods and their correlation with the incubation period. The estimated mean recovery period we obtain is 22.14 days (95\% Confidence Interval(CI): 22.00 to 22.27), and the 90th percentile is 28.91 days (95\% CI: 28.71 to 29.13), which is in agreement with statistical supported studies. The bimodal gamma distribution reveals that there are two groups of recovered individuals with a short recovery period, mean 21.02 days (95\% CI: 20.92 to 21.12), and a long recovery period, mean 38.88 days (95\% CI 38.61 to 39.15). Our study shows that the characteristic of the decease period and the recovery period are alike. From the bivariate analysis, we observe a high probability domain for recovered individuals with respect to incubation and recovery periods. A similar domain is obtained for deaths analyzing bivariate distribution of incubation and decease periods.