Maximum likelihood estimators of the location and scale parameters of the exponential distribution from a censored sample

In this note explicit expressions are given for the maximum likelihood estimators of the parameters of the two-parameter exponential distribution, when a doubly censored sample is available.     

A note on umvu estimation in the transformed chi-square family

The transformed chi-square family includes many common one-parameter continuous distributions. In that family, we give conditions under which a given function of the mean admits a minimum variance unbiased estimator and an orthogonal expansion for this estimator in terms of the generalized Laguerre polynomials. We show that such expansion is useful for obtaining bounds for the variance and for the study of the asymptotic properties of the unbiased estimators.     

On umvu estimators for the multivariate lognormal distribution and their variances

Uniformly minimum variance unbiased estimators of several parameters of the multivariate lognormal distribution are expressed by using the hypergeometric functions of matrix argument. And the variances are given in special cases.     

On estimation of the PDF and CDF of the Lindley distribution

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.     

Some unbiased estimators versus mean per unit and ratio estimators in finite population sample surveys

We present some unbiased estimators at the population mean in a finite population sample surveys with simple random sampling design where information on an auxiliary variance x positively correlated with the main variate y is available. Exact variance and unbiased estimate of the variance are computed for any sample size. These estimators are compared for their precision with the mean per unit and the ratio estimators. Modifications of the estimators are suggested to make them more precise than the mean per unit estimator or the ratio estimator regardless of the value of the population correlation coefficient between the variates x and y. Asymptotic distribution of our estimators and confidnece intervals for the population mean are also obtained.     

Limiting admissible estimators for variance components

Simultaneous estimation of the vector of the variance components for mixed and random models under the quadratic loss function is considered. For a large class of such models there are identified classes of admissible biased invariant quadratic estimators that are better than some admissible unbiased estimators. Numerous numerical results presented in the paper show that for many of the commonly used balanced models the improvements in the quadratic risk may be considerable over a large set of the parameter space.     

On estimating a function of the mean of a multivariate normal distribution

The unique minimum variance of unbiased estimator is obtained for analysis functions of the mean of a multivariate normal distribution with either unknown covariance matrix or with covariance matrix of the form σ²v where σ² is unknown.     

On the cohen-sackrowitz estimator of a common mean

The paper reconsider certain estimators proposed by COHENand SACKROWITZ[Ann.Statist.(1974)2,1274-1282,Ann.Statist.4,1294]for the common mean of two normal distributions on the basis of independent samples of equal size from the two populations. It derives the ncecessary and sufficient condition for improvement over the first sample mean, under squared error loss, for any member of a class containing these. It shows that the estimator proposded by them for simultaneous improvement over botyh sample means has the desired property if and only if the common size of the samples is at least nine. The requirement is milder than that for any other estimator at the present state of knolwledge and may be constrasted with their result which implies the desired property of the estimator only if the common size of the samples is at least fifteen. Upper bounds for variances if the estimators derived by them are also improved     

Anova and minque type of estimators for the one-way random effects model

The one-way random effects model with unequal variances and unequal sample sizes is considered. Estimation of the variances, variance of a single observation (total variance), and the standard error of the unweighted mean are considered. Precision of the Analysis of Variance and Unweighted Sums of Squares type of estimators and the Minimum Norm Quadratic Unbiased Estimators with a priori weights are examined.     

A note on minimum variance unbiased estimators of power series distributions

We give a simple theorem which easily enables us to get the minimum variance unbiased estimators of manv useful parametric functions of the parmecer in a left cruncated power series distribution. The theorem can be used in both cases:when the truncation is know and (ii) when truncation point is unknown.     

A comparison of various estimators of the mean of an inverse gaussian distribution

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.     

A precise estimator for the log-normal mean

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.     

On moments of dual generalized order statistics from Topp-Leone distribution

In this paper, we have derived exact and explicit expressions for the ratio and inverse moments of dual generalized order statistics from Topp-Leone distribution. This result includes the single and product moments of order statistics and lower records . Further, based on n dual generalized order statistics, we have deduced the expression for Maximum likelihood estimator (MLE) and Uniformly minimum variance unbiased estimator (UMVUE) for the shape parameter of Topp-Leone distribution. Finally, based on order statistics and lower records, a simulation study is being carried out to check the efficiency of these estimators.     

On the optimality of the sample variance

The present paper explores the structure of linear exponential families for which the sample variance is a uniformly minimum variance unbiased estimator.     

Improved estimation of common location of two exponential populations with order restricted scale parameters using censored samples

ABSTRACT

Estimation 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.     

On the relative behavior of estimators of reliability/survivability

Based on a decomposition of mean absolute error, a twofold technique is introduced whereby a pairwise comparison of point estimators of reliability/survivability can be made. Given two such estimators, the method examines (a) the “odds” in favor of one of the estimators being closer to the true value than is the other and (b) each estimator’s average closeness to the true value not only when it is closer than is the other but also when it is not. Joint consideration of these concepts is shown to form a basis for determining which of the two estimators is preferred in a given situation. An application of the theory is made by comparing the maximum likelihood and minimum variance unbiased estimators of reliability/survivability in the exponential failure model.     

On the minimum mean squared error estimators in a regression model

In this paper we analyze the properties of two estimators oroposed by Farebrother (1975) for linear regression models.     

Point estimation of the stress–strength reliability parameter for parallel system with independent and non-identical components

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.     

On the construction of nonparametric density function estimators using the bootstrap

The derivation of a new class of nonparametric density function estimators, the so-called bootstrap functional estimators (BFE's), is given. These estimators are shown to be strongly consistent under fairly nonrestrictive conditions. Some small-sample properties are discussed and a number of graphs are presented.     

A note on the estimation of variance of sample mean Using the knowledge of coefficient of variation in normal population

A class of estimators for the variance of sample mean is defined and its properties are studied in case of normal population. It is identified that the usual unbiased estimator, Singh, Pandey and Hirano (1973) -type estimator and Lee (1931) estimator are particular members of the proposed class of estimators. It is found that the minimum Mean Squared Error (MSE) of the proposed class of estimators is less than that of other estimators.