In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and sta...In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.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
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
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
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
The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved li...The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.展开更多
We study the two-action problem in the exponential distribution via empirical Bayes (EB) approach. Based on type Ⅱ censored samples, we construct an EB test rule and obtain an optimal rate of convergence which much...We study the two-action problem in the exponential distribution via empirical Bayes (EB) approach. Based on type Ⅱ censored samples, we construct an EB test rule and obtain an optimal rate of convergence which much improves the existing results in the literature.展开更多
A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and rel...A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate(MLE) parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.展开更多
This paper introduces a new distribution based on the exponential distribution, known as Size-biased Double Weighted Exponential Distribution (SDWED). Some characteristics of the new distribution are obtained. Plots f...This paper introduces a new distribution based on the exponential distribution, known as Size-biased Double Weighted Exponential Distribution (SDWED). Some characteristics of the new distribution are obtained. Plots for the cumulative distribution function, pdf and hazard function, tables with values of skewness and kurtosis are provided. As a motivation, the statistical application of the results to a problem of ball bearing data has been provided. It is observed that the new distribution is skewed to the right and bears most of the properties of skewed distribution. It is found that our newly proposed distribution fits better than size-biased Rayleigh and Maxwell distributions and many other distributions. Since many researchers have studied the procedure of the weighted distributions in the estates of forest, biomedicine and biostatistics etc., we hope in numerous fields of theoretical and applied sciences, the findings of this paper will be useful for the practitioners.展开更多
Generalized exponential distribution is a class of important distribution in lifedata analysis,especially in some skewed lifedata.The Parameter estimation problem for generalized exponential distribution model with gr...Generalized exponential distribution is a class of important distribution in lifedata analysis,especially in some skewed lifedata.The Parameter estimation problem for generalized exponential distribution model with grouped and right-censored data is considered.The maximum likelihood estimators are obtained using the EM algorithm.Some simulations are carried out to illustrate that the proposed algorithm is effective for the model.Finally,a set of medicine data is analyzed by generalized exponential distribution.展开更多
A new generalized linear exponential distribution (NCLED) is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the ...A new generalized linear exponential distribution (NCLED) is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations (MLE) of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.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
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
Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics,however,most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponen...Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics,however,most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious period.This paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control strategies.For this purpose,we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period:the first one is an exponential distribution model(EDM),and the other one is a gamma distribution model(GDM);explicit formula of peak time of the EDM is presented via our analytical approach.By data fitting with the COVID-19(Omicron)epidemic in Spain and Norway,it seems that Spain is more suitable for EDM while Norway is more suitable for GDM.Finally,we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates,and increase of primary course rate(PCR)and booster dose rate(BDR).展开更多
Using the memoryless property of the exponential distribution, we have proved again that the relation between the Poisson process and the exponential distribution, that is, the stochastic process {N(t), t≥0} is s...Using the memoryless property of the exponential distribution, we have proved again that the relation between the Poisson process and the exponential distribution, that is, the stochastic process {N(t), t≥0} is said to be a Poisson process with arrival rate λ(】0) if and only if the sequence of interarrival times {τ n,n≥1} are independent and identically distributed according to an exponential distribution with parameter λ, where N(t) denotes the arrival number in (0,t\].. It′s noting that the proof provided in this paper is concise and intuitive.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
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
In this paper, a new distribution called Marshall-Olkin Exponentiated Fréchet distribution (MOEFr) is proposed. The goal is to increase the flexibility of the existing Exponentiated Fréchet distribution by i...In this paper, a new distribution called Marshall-Olkin Exponentiated Fréchet distribution (MOEFr) is proposed. The goal is to increase the flexibility of the existing Exponentiated Fréchet distribution by including an extra shape parameter, resulting into a more flexible distribution that can provide a better fit to various data sets than the baseline distribution. A generator method introduced by Marshall and Olkin is used to develop the new distribution. Some properties of the new distribution such as hazard rate function, survival function, reversed hazard rate function, cumulative hazard function, odds function, quantile function, moments and order statistics are derived. The maximum likelihood estimation is used to estimate the model parameters. Monte Carlo simulation is used to evaluate the behavior of the estimators through the average bias and root mean squared error. The new distribution is fitted and compared with some existing distributions such as the Exponentiated Fréchet (EFr), Marshall-Olkin Fréchet (MOFr), Beta Exponential Fréchet (BEFr), Beta Fréchet (BFr) and Fréchet (Fr) distributions, on three data sets, namely Bladder cancer, Carbone and Wheaton River data sets. Based on the goodness-of-fit statistics and information criteria values, it is demonstrated that the new distribution provides a better fit for the three data sets than the other distributions considered in the study.展开更多
文摘In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.
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.
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.
文摘The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.
文摘We study the two-action problem in the exponential distribution via empirical Bayes (EB) approach. Based on type Ⅱ censored samples, we construct an EB test rule and obtain an optimal rate of convergence which much improves the existing results in the literature.
基金supported by the Research Center of the Female Scientific and Medical Colleges,Deanship of Scientific Research,King Saud University
文摘A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate(MLE) parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.
文摘This paper introduces a new distribution based on the exponential distribution, known as Size-biased Double Weighted Exponential Distribution (SDWED). Some characteristics of the new distribution are obtained. Plots for the cumulative distribution function, pdf and hazard function, tables with values of skewness and kurtosis are provided. As a motivation, the statistical application of the results to a problem of ball bearing data has been provided. It is observed that the new distribution is skewed to the right and bears most of the properties of skewed distribution. It is found that our newly proposed distribution fits better than size-biased Rayleigh and Maxwell distributions and many other distributions. Since many researchers have studied the procedure of the weighted distributions in the estates of forest, biomedicine and biostatistics etc., we hope in numerous fields of theoretical and applied sciences, the findings of this paper will be useful for the practitioners.
文摘Generalized exponential distribution is a class of important distribution in lifedata analysis,especially in some skewed lifedata.The Parameter estimation problem for generalized exponential distribution model with grouped and right-censored data is considered.The maximum likelihood estimators are obtained using the EM algorithm.Some simulations are carried out to illustrate that the proposed algorithm is effective for the model.Finally,a set of medicine data is analyzed by generalized exponential distribution.
基金Partially supported by National Natural Science Foundation of China(No.11271368)Beijing Philosophy and Social Science Foundation Grant(No.12JGB051)+2 种基金Project of Ministry of Education supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130004110007)The Key Program of National Philosophy and Social Science Foundation Grant(No.13AZD064)China Statistical Research Project(No.2011LZ031)
文摘A new generalized linear exponential distribution (NCLED) is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations (MLE) of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.
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(12271401,11871179,11771128,12171291)the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(20200001)the Fundamental Research Program of Shanxi Province(202103021224018).
文摘Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics,however,most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious period.This paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control strategies.For this purpose,we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period:the first one is an exponential distribution model(EDM),and the other one is a gamma distribution model(GDM);explicit formula of peak time of the EDM is presented via our analytical approach.By data fitting with the COVID-19(Omicron)epidemic in Spain and Norway,it seems that Spain is more suitable for EDM while Norway is more suitable for GDM.Finally,we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates,and increase of primary course rate(PCR)and booster dose rate(BDR).
文摘Using the memoryless property of the exponential distribution, we have proved again that the relation between the Poisson process and the exponential distribution, that is, the stochastic process {N(t), t≥0} is said to be a Poisson process with arrival rate λ(】0) if and only if the sequence of interarrival times {τ n,n≥1} are independent and identically distributed according to an exponential distribution with parameter λ, where N(t) denotes the arrival number in (0,t\].. It′s noting that the proof provided in this paper is concise and intuitive.
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.
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.
文摘In this paper, a new distribution called Marshall-Olkin Exponentiated Fréchet distribution (MOEFr) is proposed. The goal is to increase the flexibility of the existing Exponentiated Fréchet distribution by including an extra shape parameter, resulting into a more flexible distribution that can provide a better fit to various data sets than the baseline distribution. A generator method introduced by Marshall and Olkin is used to develop the new distribution. Some properties of the new distribution such as hazard rate function, survival function, reversed hazard rate function, cumulative hazard function, odds function, quantile function, moments and order statistics are derived. The maximum likelihood estimation is used to estimate the model parameters. Monte Carlo simulation is used to evaluate the behavior of the estimators through the average bias and root mean squared error. The new distribution is fitted and compared with some existing distributions such as the Exponentiated Fréchet (EFr), Marshall-Olkin Fréchet (MOFr), Beta Exponential Fréchet (BEFr), Beta Fréchet (BFr) and Fréchet (Fr) distributions, on three data sets, namely Bladder cancer, Carbone and Wheaton River data sets. Based on the goodness-of-fit statistics and information criteria values, it is demonstrated that the new distribution provides a better fit for the three data sets than the other distributions considered in the study.