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Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples
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作者 WANG Liang SHI Yi-min CHANG Ping 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期54-58,共5页
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
关键词 two-parameter exponential distribution wavelets estimation empirical Bayes test asymptotic optimality convergence rates
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BAYESIAN PREDICTION FOR THE TWO-PARAMETER EXPONENTIAL DISTRIBUTION BASED ON TYPE Ⅱ DOUBLY CENSORING
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作者 LiYanling ZhaoXuanmin XieWenxian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第1期75-84,共10页
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
关键词 type doubly censoring two-parameter exponential distribution Bayesian prediction Monte Carlo method.
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The Modi Exponentiated Exponential Distribution
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作者 Antoine Dieudonné Ndayisaba Leo Odiwuor Odongo Anthony Ngunyi 《Journal of Data Analysis and Information Processing》 2023年第4期341-359,共19页
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
关键词 Modi Family exponentiated exponential distribution Maximum Likelihood Estimation Order Statistics MOMENTS Quantile Function
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Marshall-Olkin Exponentiated Fréchet Distribution
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作者 Aurise Niyoyunguruza Leo Odiwuor Odongo +2 位作者 Euna Nyarige Alexis Habineza Abdisalam Hassan Muse 《Journal of Data Analysis and Information Processing》 2023年第3期262-292,共31页
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
关键词 exponentiated Fréchet distribution Maximum Likelihood Estimation Marshall-Olkin Family
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NEW TECHNOLOGY FOR FAULT DIAGNOSIS BASED ON WAVELET DENOISING AND MODIFIED EXPONENTIAL TIME-FREQUENCY DISTRIBUTION 被引量:13
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作者 Wang Xinqing,Wang Yaohua,Qian Shuhua,Chen Liuhai (Engineering College of PLA University of Science and Technology) Xu Yanshen,Zhao Xiangsong (Tianjin University) 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2001年第3期262-265,共4页
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
关键词 Wavelet multi-resolution analysis DENOISING Modified exponential distribution Fault diagnosis
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Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals 被引量:11
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作者 Weian Yan Yimin Shi +1 位作者 Baowei Song Zhaoyong Mao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第4期707-714,共8页
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
关键词 binomial removal progressive censoring maximumlikelihood estimator expected experiment time generalized exponential distribution.
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CONSISTENCY OF MLE OF THE PARAMETER OF EXPONENTIAL LIFETIME DISTRIBUTION FOR RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION 被引量:18
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作者 YE ERHUA 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1995年第4期379-386,共8页
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
关键词 Random censoring test with incomplete information exponential distribution maximum likelihood estimator consistency.
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Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems 被引量:4
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作者 Li Hecheng Wang Yuping 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第6期1157-1164,共8页
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
关键词 mixed-integer nonlinear bilevel programming genetic algorithm exponential distribution optimalsolutions
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STRUCTURES OF SYSTEMS WITH EXPONENTIAL LIFE DISTRIBUTIONS 被引量:3
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作者 CAI JUN WU YANHONG Department of Mathematics, Teacher’s College of Yanzhou University Yangzhou 225002 Current address: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada. Department of Mathematical Sciences,University of Alberta, Edmonton, Alberta, T6G 2G1, Canada. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第1期51-58,共8页
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
关键词 Monotone system cold standby system multivariate exponential distribution NBUHNBUE.
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Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS 被引量:1
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作者 Amer I.Al-Omari Amal S.Hassan +2 位作者 Heba F.Nagy Ayed R.A.Al-Anzi Loai Alzoubi 《Computers, Materials & Continua》 SCIE EI 2021年第12期3795-3811,共17页
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
关键词 Shannon entropy generalized inverse exponential distribution Bayesian estimators loss function ranked set sampling markov chain
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STATISTICAL INFERENCE FOR A BIVARIATE EXPONENTIAL DISTRIBUTION BASED ON GROUPED DATA
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作者 YE CINAN(Department of Applied Mathematics, Naming University of Science & Tech.nology, Naming210014.) 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第3期285-294,共10页
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
关键词 Bivariate exponential distribution parameter estimation grouped data asymptoticproperty.
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Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions
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作者 Frederic von Wegner 《Applied Mathematics》 2014年第13期2050-2056,共7页
A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Ran... A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems. 展开更多
关键词 Heavy-Tailed distributionS Random Sampling GAUSSIAN exponential POWER-LAW
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Some Moments of Linear Combination of Marshall and Olinkin’s Biviariate Exponential Distribution 被引量:1
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作者 Yunfei Guo 《信息工程期刊(中英文版)》 2015年第5期12-15,共4页
关键词 马歇尔 分发 线性
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Characterization of Negative Exponential Distribution through Expectation
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作者 Milind Bhatt B. 《Open Journal of Statistics》 2013年第5期367-369,共3页
For characterization of negative exponential distribution one needs any arbitrary non-constant function only in place of approaches such as identical distributions, absolute continuity, constant regression of order st... For characterization of negative exponential distribution one needs any arbitrary non-constant function only in place of approaches such as identical distributions, absolute continuity, constant regression of order statistics, continuity and linear regression of order statistics, non-degeneracy etc. available in the literature. Path breaking different approach for characterization of negative exponential distribution through expectation of non-constant function of random variable is obtained. An example is given for illustrative purpose. 展开更多
关键词 CHARACTERIZATION NEGATIVE exponential distribution
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Monotone Empirical Bayes Test for the Exponential Distribution
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作者 王立春 《Northeastern Mathematical Journal》 CSCD 2006年第3期265-274,共10页
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
关键词 empirical Bayes exponential distribution rate of convergence
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Robust and Efficient Reliability Estimation for Exponential Distribution
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作者 Muhammad Aslam Mohd Safari Nurulkamal Masseran Muhammad Hilmi Abdul Majid 《Computers, Materials & Continua》 SCIE EI 2021年第11期2807-2824,共18页
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
关键词 exponential distribution M-ESTIMATOR probability integral transform statistic robust estimation RELIABILITY
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The Beta Power Exponential Distribution
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作者 Kazeem A. Adepoju Chukwu, A.U Min Wang 《Journal of Statistical Science and Application》 2014年第1期37-46,共10页
A new three-parameter beta power distribution is introduced and studied. We derive formal expressions for its moments, generating function and Cumulative density function. The maximum likelihood estimation of the mode... A new three-parameter beta power distribution is introduced and studied. We derive formal expressions for its moments, generating function and Cumulative density function. The maximum likelihood estimation of the model parameters was also conducted. In the end, the superiority of the new distribution over the exponentiated exponential was made by means of data set. 展开更多
关键词 exponential distribution Beta power exponential exponentiated exponential maximum likelihood
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The Exponential Flexible Weibull Extension Distribution
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作者 Beih S. El-Desouky Abdelfattah Mustafa Shamsan Al-Garash 《Open Journal of Modelling and Simulation》 2017年第1期83-97,共15页
This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-sha... This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-shaped hazard rate function. Some statistical properties such as the mode, median, the moment, quantile function, the moment generating function and order statistics are discussed. Moreover, the maximum likelihood method for estimating the model parameters and the Fisher’s information matrix is given. Finally, the advantage of the EFWE distribution is concluded by an application using real data. 展开更多
关键词 exponential FLEXIBLE Weibull exponential distribution FLEXIBLE Weibull distribution exponential Weibull RELIABILITY MOMENTS Estimation
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On Moment Generating Function of Generalized Order Statistics from Erlang-Truncated Exponential Distribution
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作者 Anamika Kulshrestha R. U. Khan Devendra Kumar 《Open Journal of Statistics》 2012年第5期557-564,共8页
In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The resul... In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed. 展开更多
关键词 Generalized Order STATISTICS Order STATISTICS Record Values Erlang-Truncated exponential distribution MARGINAL and Joint MOMENT Generating Function RECURRENCE Relations and Characterization
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Modeling the Interior of Black Holes Utilizing a 4-D Spatial Blackbody Radiation Model with an Exponential Distribution
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作者 Christopher Pilot 《Journal of High Energy Physics, Gravitation and Cosmology》 2019年第3期953-983,共31页
This is a second follow up paper on a model, which treats the black hole as a 4-D spatial ball filled with blackbody radiation. For the interior radiative mass distribution, we employ a new type of truncated probabili... This is a second follow up paper on a model, which treats the black hole as a 4-D spatial ball filled with blackbody radiation. For the interior radiative mass distribution, we employ a new type of truncated probability distribution function, the exponential distribution. We find that this distribution comes closest to reproducing a singularity at the center, and yet it is finite at 4-D radius, . This distribution will give a constant gravitational acceleration for a test particle throughout the black hole, irrespective of radius. The 4-D gravitational acceleration is given by the expression, , where R is the radius of the black hole, MR is its mass, and is the exponential shape parameter, which depends only on the mass, or radius, of the black hole. We calculate the gravitational force, and the entropy within the black hole interior, as well as on its surface, identified as the event horizon, which separates 3-D from 4-D space. Similar to a truncated Gaussian distribution, the gravitational force increases discontinuously, and dramatically, upon entry into the 4-D black hole from the 3-D side. It is also radius dependent within the 4-D black hole. Moreover, the total entropy is shown to be much less than the Bekenstein result, similar to the truncated Gaussian. For the gravitational force, we obtain, , where Mr is the radiative mass enclosed within a 4-D volume of radius r. This unusual force law indicates that the gravitational force acting upon a layer of blackbody photons at radius r is strictly proportional to the enclosed radiative energy, MrC2, contained within that radius, with 0.1λ being the constant of proportionality. For the entropy at radius, r, and on the surface, we obtain an expression which is order of magnitude comparable to the truncated Normal distribution. Tables are presented for three black holes, one having a mass equal to that of the sun. The other two have masses, which are ten times that of the sun, and 106 solar masses. The corresponding parameters are found to equal, , respectively. We compare these results to the truncated Gaussian distribution, which were worked out in another paper. 展开更多
关键词 Black HOLES 4-D SPATIAL BLACKBODY Radiation Model exponential distribution
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