共查询到20条相似文献,搜索用时 15 毫秒
1.
This article addresses two methods of estimation of the probability density function (PDF) and cumulative distribution function (CDF) for the Lindley distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE) and maximum likelihood estimator (MLE). Since the Lindley distribution is more flexible than the exponential distribution, the same estimators have been found out for the exponential distribution and compared. Monte Carlo simulations and a real data analysis are performed to compare the performances of the proposed methods of estimation. 相似文献
2.
Zohreh Pakdaman 《统计学通讯:模拟与计算》2018,47(4):1193-1203
In this article, the estimation problem of the multicomponent stress–strength reliability parameter is considered where the stress and the strength systems have arbitrary fixed numbers of independent and non-identical parallel components. It is assumed that the distribution functions of the stress and the strength components satisfy the proportional reversed hazard rate model. The study is done in more details when the baseline distributions are exponential. Maximum likelihood and uniformly minimum variance unbiased estimators are obtained and compared. Also, Bayes and empirical Bayes estimators are discussed and Monte Carlo simulations are carried out to compare their performances. 相似文献
3.
Consider the problem of estimating the common location parameter of two exponential populations using record data when the scale parameters are unknown. We derive the maximum likelihood estimator (MLE), the modified maximum likelihood estimator (MMLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the common location parameter. Further, we derive a general result for inadmissibility of an equivariant estimator under the scaled-squared error loss function. Using this result, we conclude that the MLE and the UMVUE are inadmissible and better estimators are provided. A simulation study is conducted for comparing the performances of various competing estimators. 相似文献
4.
This article deals with the estimation of the stress-strength parameter R = P(Y < X) when X and Y are independent Lindley random variables with different shape parameters. The uniformly minimum variance unbiased estimator has explicit expression, however, its exact or asymptotic distribution is very difficult to obtain. The maximum likelihood estimator of the unknown parameter can also be obtained in explicit form. We obtain the asymptotic distribution of the maximum likelihood estimator and it can be used to construct confidence interval of R. Different parametric bootstrap confidence intervals are also proposed. Bayes estimator and the associated credible interval based on independent gamma priors on the unknown parameters are obtained using Monte Carlo methods. Different methods are compared using simulations and one data analysis has been performed for illustrative purposes. 相似文献
5.
In the model of progressive type II censoring, point and interval estimation as well as relations for single and product moments are considered. Based on two-parameter exponential distributions, maximum likelihood estimators (MLEs), uniformly minimum variance unbiased estimators (UMVUEs) and best linear unbiased estimators (BLUEs) are derived for both location and scale parameters. Some properties of these estimators are shown. Moreover, results for single and product moments of progressive type II censored order statistics are presented to obtain recurrence relations from exponential and truncated exponential distributions. These relations may then be used to compute all the means, variances and covariances of progressive type II censored order statistics based on exponential distributions for arbitrary censoring schemes. The presented recurrence relations simplify those given by Aggarwala and Balakrishnan (1996) 相似文献
6.
Ajit Chaturvedi 《统计学通讯:理论与方法》2019,48(3):537-548
This paper presents the extension of the inferences on the stress-strength reliability in more than two states to the system depending on the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. The main objective of present paper is to consider different method of estimation, under Type II censoring, for the stress-strength models and to compare them, in more than two states, to the system depending on the ratio of the strength and stress values, when the stress and strength follow independent Weibull distributions, sharing the common shape parameter α. 相似文献
7.
《Journal of Statistical Computation and Simulation》2012,82(1-2):71-81
In this paper we consider the Inverse Gaussian distribution whose variance is proportional to the mean. Assuming that the data are available from IGD(,μ,c,μ 2), and also from its length biased version, simulation studies are presented to compare the MVUE and MLE in terms of their variances and mean square errors from both kinds of data. Some tables and graphs are provided to analyze the comparisons. Finally, some recommendations and conclusions are given when one or both kinds of data are available. 相似文献
8.
In this article, we present characterizations, associated with the stress?strength reliability, of distributions with some general exponential and general inverse exponential forms. We obtain a general form for stress?strength reliability, when the distributions of the stress and the strength are non identical and independently distributed with either form. We obtain different point and interval estimators of stress?strength reliability. The theoretical results obtained can be directly applied whenever the distributions of the stress and the strength possess the forms discussed. A simulation study is carried out showing satisfactory performance of the estimators obtained. Moreover, a real data example is presented. 相似文献
9.
Shirin Shoaee 《统计学通讯:理论与方法》2013,42(24):5306-5328
Based on progressively Type-II censored samples, this article deals with inference for the stress-strength reliability R = P(Y < X) when X and Y are two independent two-parameter bathtub-shape lifetime distributions with different scale parameters, but having the same shape parameter. Different methods for estimating the reliability are applied. The maximum likelihood estimate of R is derived. Also, its asymptotic distribution is used to construct an asymptotic confidence interval for R. Assuming that the shape parameter is known, the maximum likelihood estimator of R is obtained. Based on the exact distribution of the maximum likelihood estimator of R an exact confidence interval of that has been obtained. The uniformly minimum variance unbiased estimator are calculated for R. Bayes estimate of R and the associated credible interval are also got under the assumption of independent gamma priors. Monte Carlo simulations are performed to compare the performances of the proposed estimators. One data analysis has been performed for illustrative purpose. Finally, we will generalize this distribution to the proportional hazard family with two parameters and derive various estimators in this family. 相似文献
10.
ABSTRACTBased on record values, this article deals with inference for stress–strength reliability, R = P(X < Y), where the distributions of X and Y follow proportional hazard rate models but having different parameters. Maximum likelihood estimator, uniformly minimum variance unbiased estimator, Bayes estimator, and different confidence intervals for R are obtained. Numerical computations and simulation study are presented for illustrative purposes. 相似文献
11.
Log-normal linear models are widely used in applications, and many times it is of interest to predict the response variable or to estimate the mean of the response variable at the original scale for a new set of covariate values. In this paper we consider the problem of efficient estimation of the conditional mean of the response variable at the original scale for log-normal linear models. Several existing estimators are reviewed first, including the maximum likelihood (ML) estimator, the restricted ML (REML) estimator, the uniformly minimum variance unbiased (UMVU) estimator, and a bias-corrected REML estimator. We then propose two estimators that minimize the asymptotic mean squared error and the asymptotic bias, respectively. A parametric bootstrap procedure is also described to obtain confidence intervals for the proposed estimators. Both the new estimators and the bootstrap procedure are very easy to implement. Comparisons of the estimators using simulation studies suggest that our estimators perform better than the existing ones, and the bootstrap procedure yields confidence intervals with good coverage properties. A real application of estimating the mean sediment discharge is used to illustrate the methodology. 相似文献
12.
Kōsei Iwase 《统计学通讯:理论与方法》2013,42(12):3559-3566
The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator. 相似文献
13.
Maximum likelihood and uniform minimum variance unbiased estimators of steady-state probability distribution of system size, probability of at least ? customers in the system in steady state, and certain steady-state measures of effectiveness in the M/M/1 queue are obtained/derived based on observations on X, the number of customer arrivals during a service time. The estimators are compared using Asympotic Expected Deficiency (AED) criterion leading to recommendation of uniform minimum variance unbiased estimators over maximum likelihood estimators for some measures. 相似文献
14.
A precise estimator for the log-normal mean 总被引:2,自引:0,他引:2
The log-normal distribution is frequently encountered in applications. The uniformly minimum variance unbiased (UMVU) estimator for the log-normal mean is given explicitly by a formula found by Finney in 1941. In contrast to this the most commonly used estimator for a log-normal mean is the sample mean. This is possibly due to the complexity of the formula given by Finney. A modified maximum likelihood estimator which approximates the UMVU estimator is derived here. It is sufficiently simple to be implemented in elementary spreadsheet applications. An elementary approximate formula for the root-mean-square error of the suggested estimator and the UMVU estimator is presented. The suggested estimator is compared with the sample mean, the maximum likelihood, and the UMVU estimators by Monte Carlo simulation in terms of root-mean-square error. 相似文献
15.
Milan Jovanović 《统计学通讯:模拟与计算》2017,46(4):3050-3066
This article deals with the estimation of R = P{X < Y}, where X and Y are independent random variables from geometric and exponential distribution, respectively. For complete samples, the MLE of R, its asymptotic distribution, and confidence interval based on it are obtained. The procedure for deriving bootstrap-p confidence interval is presented. The UMVUE of R and UMVUE of its variance are derived. The Bayes estimator of R is investigated and its Lindley's approximation is obtained. A simulation study is performed in order to compare these estimators. Finally, all point estimators for right censored sample from the exponential distribution, are obtained. 相似文献
16.
《Journal of Statistical Computation and Simulation》2012,82(11):2345-2360
The uniformly minimum variance unbiased, maximum-likelihood, percentile and least-squares estimators of the probability density function and the cumulative distribution function are derived for the generalized exponential-Poisson distribution. This model has shown to be useful in reliability and lifetime data modelling, especially when the hazard rate function has a bathtub shape. Simulation studies are also carried out to show that the maximum-likelihood estimator is better than the uniformly minimum variance unbiased estimator (UMVUE) and that the UMVUE is better than others. 相似文献
17.
Kōsei Iwase 《统计学通讯:理论与方法》2013,42(5):1315-1320
The uniformly minimum variance unbiased estimator and the maximum likelihood estimator of μ for the inverse Gaussian distribution I(μc,μ ) with known c are constructed, and they are shown to be asymptoti- cally equivalent. 相似文献
18.
Manas Ranjan Tripathy 《统计学通讯:模拟与计算》2013,42(9):2800-2818
ABSTRACTEstimation of common location parameter of two exponential populations is considered when the scale parameters are ordered using type-II censored samples. A general inadmissibility result is proved which helps in deriving improved estimators. Further, a class of estimators dominating the MLE has been derived by an application of integrated expression of risk difference (IERD) approach of Kubokawa. A discussion regarding extending the results to a general k( ? 2) populations has been done. Finally, all the proposed estimators are compared through simulation. 相似文献
19.
Badiollah R. Asrabadi 《统计学通讯:理论与方法》2013,42(3):713-733
The exact distribution of the sample median, and of the maximum likelihood estimator of the scale parameter of the Laplace distribution is derived. Tables of Teans, variances and the distribution functions of the corresponding dislributions are evaluacted. Exact ,solutions to the problem of confidence interval and hypothesrs testing for the scale paramrter are provided. The minimum variance unbiased estimator (MVUE) of the p.d.f. of the Laplace distribution when the location parameter is known is also given. 相似文献
20.
Micha Mandel 《The American statistician》2020,74(1):98-100
AbstractSufficiency, conditionality, and invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to teach modern methods. However, being the philosophical cornerstones of statistical inference, a minimal understanding of these principles should be part of any curriculum in statistics. The scaled uniform model is used here to demonstrate the importance and usefulness of the conditionality principle, which is probably the most basic and less familiar among the three. 相似文献