ESTIMATION OF GUARANTEE TIME AND MEAN LIFE AFTER WARRANTY FOR TWO-PARAMETER EXPONENTIAL FAILURE MODEL

Suppose manufactured items have failure times distributed with the two-parameter exponential density function à-^le-(x-μ)/à (x≥μ≥0). The paper considers estimation of the guarantee time μ and mean life after warranty à. Properties of various estimators are given for both separate and simultaneous estimation of μ and à. Criteria for comparing estimators are entropy loss, LINEX loss, and (generalized) Pitman nearness.     

Estimation for the generalized half-normal distribution based on progressive type-II censoring

Based on progressively type-II censored data, the problem of estimating unknown parameters and reliability function of a two-parameter generalized half-normal distribution is considered. Maximum likelihood estimates are obtained by applying expectation-maximization algorithm. Since they do not have closed forms, approximate maximum likelihood estimators are proposed. Several Bayesian estimates with respect to different symmetric and asymmetric loss functions such as squared error, LINEX and general entropy are calculated. The Lindley approximation method is applied to determine Bayesian estimates. Monte Carlo simulations are performed to compare the performances of the different methods. Finally, one real data set is analysed.     

Estimation of the smaller and larger of two uniform scale parameters

Assume independent random samples are drawn from two populations which are uniformly distributed with unknown scale parameters. The problem is to estimate the minimum and the maximum of the two unknown scales. In this paper, several simple estimators are proposed which are better than the natural estimators in terms of standardized bias, risk under squared error loss and the Pitman nearness criterion.     

Estimation using hybrid censored data from a generalized inverted exponential distribution

ABSTRACT

We consider point and interval estimation of the unknown parameters of a generalized inverted exponential distribution in the presence of hybrid censoring. The maximum likelihood estimates are obtained using EM algorithm. We then compute Fisher information matrix using the missing value principle. Bayes estimates are derived under squared error and general entropy loss functions. Furthermore, approximate Bayes estimates are obtained using Tierney and Kadane method as well as using importance sampling approach. Asymptotic and highest posterior density intervals are also constructed. Proposed estimates are compared numerically using Monte Carlo simulations and a real data set is analyzed for illustrative purposes.     

Generalized varying-coefficient single-index model

In this paper, the generalized varying-coefficient single-index model is discussed based on penalized likelihood. All the unknown functions are fitted by penalized spline. The estimates of the unknown parameters and the unknown coefficient functions are obtained and the estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. Two simulation studies are carried out to illustrate the performance of the estimates. An application of the model to the Hong Kong environmental data further demonstrates the potential of the proposed modelling procedures.     

Admissibility of estimators in the non-regular family under entropy loss function

In this paper we have considered the problem of finding admissible estimates for a fairly general class of parametric functions in the so called “non-regular” type of densities. The admissibility of generalized Bayes and Pitman estimates of functions of parameters have been established under entropy loss function.     

Robust estimation of extremes

We consider the problem of making inferences about extreme values from a sample. The underlying model distribution is the generalized extreme-value (GEV) distribution, and our interest is in estimating the parameters and quantiles of the distribution robustly. In doing this we find estimates for the GEV parameters based on that part of the data which is well fitted by a GEV distribution. The robust procedure will assign weights between 0 and 1 to each data point. A weight near 0 indicates that the data point is not well modelled by the GEV distribution which fits the points with weights at or near 1. On the basis of these weights we are able to assess the validity of a GEV model for our data. It is important that the observations with low weights be carefully assessed to determine whether diey are valid observations or not. If they are, we must examine whether our data could be generated by a mixture of GEV distributions or whether some other process is involved in generating the data. This process will require careful consideration of die subject matter area which led to the data. The robust estimation techniques are based on optimal B-robust estimates. Their performance is compared to the probability-weighted moment estimates of Hosking et al. (1985) in both simulated and real data.     

Estimation of parameters of Kumaraswamy-Exponential distribution under progressive type-II censoring

In this paper, the problem of estimating unknown parameters of a two-parameter Kumaraswamy-Exponential (Kw-E) distribution is considered based on progressively type-II censored sample. The maximum likelihood (ML) estimators of the parameters are obtained. Bayes estimates are also obtained using different loss functions such as squared error, LINEX and general entropy. Lindley's approximation method is used to evaluate these Bayes estimates. Monte Carlo simulation is used for numerical comparison between various estimates developed in this paper.     

Admissibility of generalized bayes and pitman estimates in the non-regular family

In this paper we have considered the problem of finding admissible estimates for a fairly general class of parametric functions in the so called “non-regular” type of densities Following Karlin s (1958) technique, we have established the ad-missibility of generalized Bayes estimates and Pitman estimates. Some examples are discussed.     

Construction of Simultaneous Confidence Intervals for Ratios of Means of Lognormal Distributions

For constructing simultaneous confidence intervals for ratios of means for lognormal distributions, two approaches using a two-step method of variance estimates recovery are proposed. The first approach proposes fiducial generalized confidence intervals (FGCIs) in the first step followed by the method of variance estimates recovery (MOVER) in the second step (FGCIs–MOVER). The second approach uses MOVER in the first and second steps (MOVER–MOVER). Performance of proposed approaches is compared with simultaneous fiducial generalized confidence intervals (SFGCIs). Monte Carlo simulation is used to evaluate the performance of these approaches in terms of coverage probability, average interval width, and time consumption.     

Power-linear models for incomplete contingency tables with nonignorable non-responses

For categorical data exhibiting nonignorable non-responses, it is well known that maximum likelihood (ML) estimates with a boundary solution are implausible and do not provide a perfect fit to the observed data even for saturated models. We provide the conditions under which ML estimates for the generalized linear model (GLM) with the usual log/logit link function have a boundary solution. These conditions introduce a new GLM with appropriately defined power link functions where its ML estimates resolve the problems arising from a boundary solution and offer useful statistics for identifying the non-response mechanism. This model is applied to a real dataset and compared with Bayesian models.     

On the inadmssibelity of ridge estimator in a linear model

The necessary and sufficient conditions for the inadmissibility of the ridge regression is discussed under two different criteria, namely, average loss and Pitman nearness. Although the two criteria are very different, same conclusions are obtained. The loss functions considered in this article are th likelihood loss function and the Mahalanobis loss function. The two loss functions are motivated from the point of view of classification of two normal populations. Under the Mahalanobis loss it is demonstrated that the ridge regression is always inadmissible as long as the errors are assumed to be symmetrically distributed about the origin.     

Comparison of estimators of a dispersion matrix under generalized pitman nearness criterion

Some equivariant estimators of the dispersion matrix of a multivariate normal population are compared using the generalized Pitman nearness criterion based on the entropy loss function. It is shown that, under the group of lower triangular transformations, a best equivariant estimator does not exist. Existence of best estimators in certain subclasses are discussed and the performances of two commonly used estimators are compared. Some properties of central chi-square distributions are obtained and used to derive the main results.     

Estimation for the Parameters of Generalized Half-normal Distribution Based on Progressive Type-I Interval Censoring

Based on progressively Type-I interval censored sample, the problem of estimating unknown parameters of a two parameter generalized half-normal(GHN) distribution is considered. Different methods of estimation are discussed. They include the maximum likelihood estimation, midpoint approximation method, approximate maximum likelihood estimation, method of moments, and estimation based on probability plot. Several Bayesian estimates with respect to different symmetric and asymmetric loss functions such as squared error, LINEX, and general entropy is calculated. The Lindley’s approximation method is applied to determine Bayesian estimates. Monte Carlo simulations are performed to compare the performances of the different methods. Finally, analysis is also carried out for a real dataset.     

Using bootstrap method to evaluate the estimates of nicotine equivalents from linear mixed model and generalized estimating equation

Twenty-four-hour urinary excretion of nicotine equivalents, a biomarker for exposure to cigarette smoke, has been widely used in biomedical studies in recent years. Its accurate estimate is important for examining human exposure to tobacco smoke. The objective of this article is to compare the bootstrap confidence intervals of nicotine equivalents with the standard confidence intervals derived from linear mixed model (LMM) and generalized estimation equation. We use percentile bootstrap method because it has practical value for real-life application and it works well with nicotine data. To preserve the within-subject correlation of nicotine equivalents between repeated measures, we bootstrap the repeated measures of each subject as a vector. The results indicate that the bootstrapped estimates in most cases give better estimates than the LMM and generalized estimation equation without bootstrap.     

Efficiency of the generalized difference-based Liu estimators in semiparametric regression models with correlated errors

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β in the semiparametric regression model. Under the linear nonstochastic constraint Rβ=r, the generalized restricted difference-based Liu estimator is given. The risk function for the β?_GRD(η) associated with weighted balanced loss function is presented. The performance of the proposed estimators is evaluated by a simulated data set.     

Estimation for the parameters of the generalized half-normal distribution

As an applicable and flexible lifetime model, the two-parameter generalized half-normal (GHN) distribution has been received wide attention in the field of reliability analysis and lifetime study. In this paper maximum likelihood estimates of the model parameters are discussed and we also proposed corresponding bias-corrected estimates. Unweighted and weighted least squares estimates for the parameters of the GHN distribution are also presented for comparison purpose. Moreover, the likelihood ratio test is provided as complementary. Simulation study and illustrative examples are provided to compare the performance of the proposed methods.     

Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness criterion when variables are omitted

This paper compares the Stein and the usual estimators of the error variance under the Pitman nearness (PN) criterion in a regression model which is mis-specified due to missing relevant explanatory variables. The exact expression of the PN-probability is derived and numerically evaluated. Contrary to the well-known result under mean squared errors (MSE), with the PN criterion the Stein variance estimator is uniformly dominated by the usual estimator when no relevant variables are excluded from the model. With an increased degree of model mis-specification, neither estimator strictly dominates the other. The authors are grateful to two anonymous referees for their valuable comments. Also, the first author is grateful to the Japan Society for the Promotion of Science for partial financial support.     

Comparison of Two Estimators of Parameters Under Pitman Nearness Criterion

In this article, Pitman nearness criterion is used to compare two competing united biased estimators in linear model. In particular, a sufficient and necessary condition for one estimator being superior to the other is derived. Furthermore, a simulation study is performed to illustrate the theoretical results and several special cases are also studied.     

The truncated generalized poisson distribution and its estimation

A discrete probability model always gets truncated during the sampling process and the point of truncation depends upon the sample size. Also, the generalized Poisson distribution cannot be used with full justification when the second parameter is negative. To avoid these problems a truncated generalized Poisson distribution is defined and studied. Estimation of its parameters by moments method, maximum likelihood method and a mixed method are considered. Some examples are given to illustrate the effect on the parameters’ estimates when a non-truncated GPD is used instead of a truncated GPD.