Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated...Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.展开更多
A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical pro...A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.展开更多
Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE lif...Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE life distributions isessentially a series system composed of components with multivariate exponential lifedistributions. Also, it is proved that for cold standby systems composed of componentswith multivariate NBU life distributions, all but oue of the components are degenerateat zero while the remaining one is exponential. In addition, several equivalent char-acterizations of multivariate exponential distribution are provided in the multivariateHNBUE life distribution class which include many existing results as special cases.展开更多
A new family of univariate exponential slash distribution is introduced, which is based on elliptical distributions and defined by means of a stochastic representation as the scale mixture of an elliptically distribut...A new family of univariate exponential slash distribution is introduced, which is based on elliptical distributions and defined by means of a stochastic representation as the scale mixture of an elliptically distributed random variable with respect to the power of an exponential random variable. The same idea is extended to the multivariate case. General properties of the resulting families, including their moments and kurtosis coefficient, are stud- ied. And inferences based on methods of moment and maximum likelihood are discussed. A real data is presented to show this family is flexible and fits much better than other related families.展开更多
Extreme mortality bonds(EMBs),which can transfer the extreme mortality risks confronted by life insurance companies into the capital market,refer to the bonds whose nominal values or coupons are associated with mortal...Extreme mortality bonds(EMBs),which can transfer the extreme mortality risks confronted by life insurance companies into the capital market,refer to the bonds whose nominal values or coupons are associated with mortality index.This paper first provides the expected value of mortality index based on the double exponential jump diffusion(DEJD)model under the risk-neutral measure;then derives the pricing models of the EMBs with principal reimbursement non-cumulative and cumulative threshold respectively;finally simulates the bond prices and conducts a parameter sensitivity analysis.This paper finds that the jump and direction characteristics of mortality index have significant impacts on the accuracy of the EMB pricing.展开更多
The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim ...The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.展开更多
Modeling HIV/AIDS progression is critical for understanding disease dynamics and improving patient care. This study compares the Exponential and Weibull survival models, focusing on their ability to capture state-spec...Modeling HIV/AIDS progression is critical for understanding disease dynamics and improving patient care. This study compares the Exponential and Weibull survival models, focusing on their ability to capture state-specific failure rates in HIV/AIDS progression. While the Exponential model offers simplicity with a constant hazard rate, it often fails to accommodate the complexities of dynamic disease progression. In contrast, the Weibull model provides flexibility by allowing hazard rates to vary over time. Both models are evaluated within the frameworks of the Cox Proportional Hazards (Cox PH) and Accelerated Failure Time (AFT) models, incorporating critical covariates such as age, gender, CD4 count, and ART status. Statistical evaluation metrics, including Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood, and Pseudo-R2, were employed to assess model performance across diverse patient subgroups. Results indicate that the Weibull model consistently outperforms the Exponential model in dynamic scenarios, such as younger patients and those with co-infections, while maintaining robustness in stable contexts. This study highlights the trade-off between flexibility and simplicity in survival modeling, advocating for tailored model selection to balance interpretability and predictive accuracy. These findings provide valuable insights for optimizing HIV/AIDS management strategies and advancing survival analysis methodologies.展开更多
We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scen...We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scenario,in which the lifetime associated with a particular risk is not observable;rather,we observe only the maximum lifetime value among all risks.The distribution exhibits decreasing,increasing,unimodal and bathtub shaped hazard rate functions,depending on its parameters.Several properties of the EPLPS distribution are investigated.Moreover,we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix.Finally,applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.展开更多
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete informat...In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.展开更多
Fast wavelet multi-resolution analysis (wavelet MRA) provides a effective tool for analyzing and canceling disturbing components in original signal. Because of its exponential frequency axis, this method isn't s...Fast wavelet multi-resolution analysis (wavelet MRA) provides a effective tool for analyzing and canceling disturbing components in original signal. Because of its exponential frequency axis, this method isn't suitable for extracting harmonic components. The modified exponential time-frequency distribution ( MED) overcomes the problems of Wigner distribution( WD) ,can suppress cross-terms and cancel noise further more. MED provides high resolution in both time and frequency domains, so it can make out weak period impulse components fmm signal with mighty harmonic components. According to the 'time' behavior, together with 'frequency' behavior in one figure,the essential structure of a signal is revealed clearly. According to the analysis of algorithm and fault diagnosis example, the joint of wavelet MRA and MED is a powerful tool for fault diagnosis.展开更多
Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure ri...Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.展开更多
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollo...Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.展开更多
This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and up...This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.展开更多
In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator...In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.展开更多
There are two weaknesses in current researches into human casualty of ship collision.One is that the range of injuries or fatalities is restricted to the maximum number of casualties in a particular sample,which may n...There are two weaknesses in current researches into human casualty of ship collision.One is that the range of injuries or fatalities is restricted to the maximum number of casualties in a particular sample,which may not cover all the possible numbers of casualties in the future.International Maritime Organization(IMO)employed the injured or dead percentage of all the persons on board to represent casualties,but it only provided several discrete values to quantify human losses in different scenarios.The other is that the assumption that the distributions of the injuries or fatalities follow certain distribution,such as negative binomial and Poisson distributions is left to be statistically tested.Firstly,this study considers casualty rate,including injury and fatality rates,as random variables;the interval of the variables are from 0 to 1.Then,the distributions of the variables are investigated using historical data.From historical data,we can find that there are many zeros.Zeroinflated models are proved to be effective in processing data with inflated zeros.Furthermore,the probability density of the variables decreases rapidly as the casualty rate becomes larger.Thus,zero-inflated exponential distribution is assumed to fit the data.The parameters of zero-inflated exponential distribution are calibrated by maximum likelihood estimation(MLE)method.Finally,the assumption is tested by chi-square test.The zeroinflated exponential distribution can be used to generate human losses as a part of consequences in the simulation of ship collision risk.展开更多
It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponent...It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.展开更多
Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Base...Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Based on grouped data, a newestimator for λ1, λ2 and λ12 is derived and its asymptotic properties are discussed.Besides, some test procedures of equal marginals and independence are given. Asimulation result is given, too.展开更多
The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which ...The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.展开更多
文摘Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.
文摘A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.
基金This work is supported by the Natural Science Foundation of the Jiangsu Provincial Education Commission.
文摘Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE life distributions isessentially a series system composed of components with multivariate exponential lifedistributions. Also, it is proved that for cold standby systems composed of componentswith multivariate NBU life distributions, all but oue of the components are degenerateat zero while the remaining one is exponential. In addition, several equivalent char-acterizations of multivariate exponential distribution are provided in the multivariateHNBUE life distribution class which include many existing results as special cases.
基金Supported by the National Natural Science Foundation of China(Grant No.61304155)Beijing Municipal Party Committee Organization Department Talents Project(Grant No.2012D005003000005)Graduate Department of BTBU Comprehensive Reform Project to Promote Talent Cultivation(Grant No.19005428069)
文摘A new family of univariate exponential slash distribution is introduced, which is based on elliptical distributions and defined by means of a stochastic representation as the scale mixture of an elliptically distributed random variable with respect to the power of an exponential random variable. The same idea is extended to the multivariate case. General properties of the resulting families, including their moments and kurtosis coefficient, are stud- ied. And inferences based on methods of moment and maximum likelihood are discussed. A real data is presented to show this family is flexible and fits much better than other related families.
文摘Extreme mortality bonds(EMBs),which can transfer the extreme mortality risks confronted by life insurance companies into the capital market,refer to the bonds whose nominal values or coupons are associated with mortality index.This paper first provides the expected value of mortality index based on the double exponential jump diffusion(DEJD)model under the risk-neutral measure;then derives the pricing models of the EMBs with principal reimbursement non-cumulative and cumulative threshold respectively;finally simulates the bond prices and conducts a parameter sensitivity analysis.This paper finds that the jump and direction characteristics of mortality index have significant impacts on the accuracy of the EMB pricing.
文摘The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.
文摘Modeling HIV/AIDS progression is critical for understanding disease dynamics and improving patient care. This study compares the Exponential and Weibull survival models, focusing on their ability to capture state-specific failure rates in HIV/AIDS progression. While the Exponential model offers simplicity with a constant hazard rate, it often fails to accommodate the complexities of dynamic disease progression. In contrast, the Weibull model provides flexibility by allowing hazard rates to vary over time. Both models are evaluated within the frameworks of the Cox Proportional Hazards (Cox PH) and Accelerated Failure Time (AFT) models, incorporating critical covariates such as age, gender, CD4 count, and ART status. Statistical evaluation metrics, including Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood, and Pseudo-R2, were employed to assess model performance across diverse patient subgroups. Results indicate that the Weibull model consistently outperforms the Exponential model in dynamic scenarios, such as younger patients and those with co-infections, while maintaining robustness in stable contexts. This study highlights the trade-off between flexibility and simplicity in survival modeling, advocating for tailored model selection to balance interpretability and predictive accuracy. These findings provide valuable insights for optimizing HIV/AIDS management strategies and advancing survival analysis methodologies.
文摘We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scenario,in which the lifetime associated with a particular risk is not observable;rather,we observe only the maximum lifetime value among all risks.The distribution exhibits decreasing,increasing,unimodal and bathtub shaped hazard rate functions,depending on its parameters.Several properties of the EPLPS distribution are investigated.Moreover,we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix.Finally,applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
文摘In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.
文摘Fast wavelet multi-resolution analysis (wavelet MRA) provides a effective tool for analyzing and canceling disturbing components in original signal. Because of its exponential frequency axis, this method isn't suitable for extracting harmonic components. The modified exponential time-frequency distribution ( MED) overcomes the problems of Wigner distribution( WD) ,can suppress cross-terms and cancel noise further more. MED provides high resolution in both time and frequency domains, so it can make out weak period impulse components fmm signal with mighty harmonic components. According to the 'time' behavior, together with 'frequency' behavior in one figure,the essential structure of a signal is revealed clearly. According to the analysis of algorithm and fault diagnosis example, the joint of wavelet MRA and MED is a powerful tool for fault diagnosis.
基金Supported by the NNSF of China(40675023)the PHD Foundation of Guangxi Normal University.
文摘Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
基金supported by National Natural Science Foundation of China (Grant No. 50875230)
文摘Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.
基金A.R.A.Alanzi would like to thank the Deanship of Scientific Research at Majmaah University for financial support and encouragement.
文摘This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.
基金This work is supported by the Universiti Kebangsaan Malaysia[Grant Number DIP-2018-038].
文摘In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.
基金the Liberal Arts and Social Sciences Foundation of Ministry of Education in China(No.19YJCGJW003)
文摘There are two weaknesses in current researches into human casualty of ship collision.One is that the range of injuries or fatalities is restricted to the maximum number of casualties in a particular sample,which may not cover all the possible numbers of casualties in the future.International Maritime Organization(IMO)employed the injured or dead percentage of all the persons on board to represent casualties,but it only provided several discrete values to quantify human losses in different scenarios.The other is that the assumption that the distributions of the injuries or fatalities follow certain distribution,such as negative binomial and Poisson distributions is left to be statistically tested.Firstly,this study considers casualty rate,including injury and fatality rates,as random variables;the interval of the variables are from 0 to 1.Then,the distributions of the variables are investigated using historical data.From historical data,we can find that there are many zeros.Zeroinflated models are proved to be effective in processing data with inflated zeros.Furthermore,the probability density of the variables decreases rapidly as the casualty rate becomes larger.Thus,zero-inflated exponential distribution is assumed to fit the data.The parameters of zero-inflated exponential distribution are calibrated by maximum likelihood estimation(MLE)method.Finally,the assumption is tested by chi-square test.The zeroinflated exponential distribution can be used to generate human losses as a part of consequences in the simulation of ship collision risk.
基金Supported by the National Natural Science Foundations of China( 1 9631 0 4 0 ) and SSFC( o2 BTJ0 0 1 ) .
文摘It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.
文摘Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Based on grouped data, a newestimator for λ1, λ2 and λ12 is derived and its asymptotic properties are discussed.Besides, some test procedures of equal marginals and independence are given. Asimulation result is given, too.
基金Supported by the NNSF of China（70471057）Supported by the Natural Science Foundation of the Education Department of Shannxi Province（03JK065）
文摘The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.
