A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function an...A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix Ŵ, Ĉ, and Ĝ, criteria test Y<sup>2</sup>n</sub>, alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for Y<sup>2</sup>n</sub> (γ) test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05.展开更多
We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a direc...We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.展开更多
In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization ...In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.展开更多
In this paper,we determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family.We then use the machinery of variance functions to establish some limit ...In this paper,we determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family.We then use the machinery of variance functions to establish some limit theorems related to this type of convolution and involving the free additive convolution and the Boolean additive convolution.展开更多
This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1<i<n,is a leader of the(i-1)th prosumer an...This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1<i<n,is a leader of the(i-1)th prosumer and is a follower of the(i+1)th prosumer.The first player(agent)is the follower at the bottom whereas the nth is the leader at the top.The problem is described by a linear jump-diffusion system of conditional mean-field type,where the conditioning is with respect to common noise,and a quadratic cost functional involving,the square of the conditional expectation of the controls of the agents.The authors provide a semi-explicit solution of the corresponding meanfield-type hierarchical control problem with common noise.Finally,the authors illustrate the obtained result via a numerical example with two different scenarios.展开更多
文摘A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix Ŵ, Ĉ, and Ĝ, criteria test Y<sup>2</sup>n</sub>, alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for Y<sup>2</sup>n</sub> (γ) test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05.
文摘We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.
文摘In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.
基金supported by the Deanship of Scientific Research at Jouf University through research Grant No.(DSR-2021-03-03188).
文摘In this paper,we determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family.We then use the machinery of variance functions to establish some limit theorems related to this type of convolution and involving the free additive convolution and the Boolean additive convolution.
基金support from Tamkeen under the NYU Abu Dhabi Research Institute grant CG002U.S.Air Force Office of Scientific Research under Grant No.FA955017-1-0259。
文摘This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1<i<n,is a leader of the(i-1)th prosumer and is a follower of the(i+1)th prosumer.The first player(agent)is the follower at the bottom whereas the nth is the leader at the top.The problem is described by a linear jump-diffusion system of conditional mean-field type,where the conditioning is with respect to common noise,and a quadratic cost functional involving,the square of the conditional expectation of the controls of the agents.The authors provide a semi-explicit solution of the corresponding meanfield-type hierarchical control problem with common noise.Finally,the authors illustrate the obtained result via a numerical example with two different scenarios.
