Test for multiple upper outliers in an exponential sample irrespective of origin

An approach for testing multiple upper outliers with slippage alternative in an exponential sample, irrespective of origin, is discussed. The outlier detection procedure is based on a ratio of two estimates, obtained by the maximization of the two log-likelihood functions. One is the complete data log-likelihood and the other is its conditional expectation, given the regular observations. The exact null distribution of the test statistic is derived and no new table for critical values is required. A simulation study is also carried out to compare the performance of the test with the earlier work.     

Testing equality of several exponential distributions

Roy's union-intersection principle is used to develop a test procedure to test the equality of scale parameters of several exponential distributions. Upper five and one percent values of the test statistic for two and three exponential distributions are tabulated and an illustrative simulated example is qiven.     

Generalized Weighted Exponential Distribution

The new class of weighted exponential (WE) distributions obtained by Gupta and Kundu (2009) by implementing Azzalini's method to the exponential distribution. In this study, we generalize the WE distribution to a new class of generalized weighted exponential (GWE) distribution. Several statistical and reliability properties of this new class of distribution are obtained. Estimation and inference procedure for distribution parameters are investigated. Finally, we show that the proposed model can provide better fit than the recent class of weighted exponential by using two real data examples.     

A Bayesian Approach for Selecting the Best Exponential Population with Interval Censored Samples

In this article, we study the problem of selecting the best population from among several exponential populations based on interval censored samples using a Bayesian approach. A Bayes selection procedure and a curtailed Bayes selection procedure are derived. We show that these two Bayes selection procedures are equivalent. A numerical example is provided to illustrate the application of the two selection procedure. We also use Monte Carlo simulation to study performance of the two selection procedures. The numerical results of the simulation study demonstrate that the curtailed Bayes selection procedure has good performance because it can substantially reduce the duration time of life test experiment.     

Statistical analysis of type I multiply left-censored samples from exponential distribution

Left-censored data with one or more detection limits (DLs) often arise in environmental contexts. The computational procedure for the calculation of maximum likelihood estimators of the parameter for Type I multiply left-censored data from underlying exponential distribution is suggested and used considering various numbers of DLs. The expected Fisher information measure (FIM) is analytically determined and its performance is compared with sample (observed) FIM using simulations. Simulations are focused primarily on the properties of estimators for small sample sizes. Moreover, the simulations follow the possible applications of the results in the statistical analysis of real chemical data.     

Estimation procedures and prediction intervals

The starship, as an alternative or companion procedure to the bootstrap, introduced by Owen (1988), and the well known maximum likelihood estimation procedure were used to find prediction intervals for the future sample mean of an exponential distribution. Some remarks based on a simulation study are made on the differences between the two procedures.     

Simultaneous inferences for ordered exponential location parameters under unbalanced data and heteroscedasticity of scale parameters

A test procedure for testing homogeneity of location parameters against simple ordered alternative is proposed for k(k ≥ 2) members of two parameter exponential distribution under unbalanced data and heteroscedasticity of the scale parameters. The relevant one-sided and two-sided simultaneous confidence intervals (SCIs) for all k(k ? 1)/2 ordered pairwise differences of location parameters are also proposed. Simulation-based study revealed that the proposed procedure is better than the recently proposed procedure in terms of power, coverage probability, and average volume of SCIs. The implementation of proposed procedure is demonstrated through real life data.     

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.     

On grouping sets of exponential populations

Suppose we have k random samples each of size n from a two parameter exponential distribution with location parameters μ _i i=1,…,k, and where each item has the same, unknown scale parameter. A multistage procedure is developed to determine t≦k groups such that in any one group the distributions have μ_i's that are not appreciably different. The method yields a unique grouping and extends the approach of the Kumar and Pate1 test.The emphasis is on the development of a procedure based on the null sampling distribution of the maximum gap of the ordered first order statistics from exponential distributions. The procedure is based on complete ordered samples or censored (of any or of all) samples.     

Estimation in the piece-wise constant hazard rate model

The piece-wise constant hazard rate is presented along with the resulting piece-wise constant exponential model for the life times. Maximum likelihood estimation is considered for the complete life test and a life test censored at a preset time. The estimators are found along with their expected values and variances. An example from industry illustrates the estimation procedure in the special case where only two pieces are used.     

Bayesian estimation and prediction based on generalized Type-I hybrid censored sample

In this paper, we consider an exponential form for the underlying distributionand a conjugate prior, and develop a procedure for deriving the maximum likelihood and Bayesian estimators based on an observed generalized Type-I hybrid censored sample. The problems of predicting the future order statistics from the same sample and that from a future sample are also discussed from a Bayesian viewpoint. For the illustration of the developed results, the exponential and Pareto distributions are used as examples. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here.     

Asymptotic Unbiased Kernel Estimator for Line Transect Sampling

In this article, we propose a new estimator for the density of objects using line transect data. The proposed estimator combines the nonparametric kernel estimator with parametric detection function: the exponential or the half normal detection function to estimate the density of objects. The selection of the detection function depends on the testing of the shoulder condition assumption. If the shoulder condition is true then the half-normal detection function is introduced together with the kernel estimator. Otherwise, the negative exponential is combined with the kernel estimator. Under these assumptions, the proposed estimator is asymptotically unbiased and it is strongly consistent estimator for the density of objects using line transect data. The simulation results indicate that the proposed estimator is very successful in taking the advantage of the parametric detection function available.     

Estimation and Confidence Intervals for Clock Offset in Networks with Bivariate Exponential Delays

There is a large and increasing literature on statistical modeling-based estimation of the offset between two clocks. Recent work has focused on the construction of confidence intervals for offset. However, in most of this work it has been assumed that the network delays that occur during the synchronization process are independent. The network delays are often modeled as independent exponential random variables. Thus, we introduce the use of a bivariate exponential distribution to capture the anticipated correlation between the network delays and derive a maximum likelihood estimator and a confidence interval procedure for the offset parameter. We then illustrate how use of the independent model for network delays can lead to improper inference about the offset parameter.     

Development of life-test sampling plans for exponential distributions based on accelerated life testing

This paper presents a procedure for developing life-test sampling plans for exponential distributions based upon accelerated life testing(ALT). Type II censoring is assumed at each overstress level. The derived test statistic is shown to be a quotient of two independent random variables, each of which is a rational power of a Chi-square random variable. The distribution of the test statistic is characterized by the H-function, which can be numerically evaluated to obtain desired sampling plans.     

Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution based on the multiply type II censored sample

Process capability indices have been widely used to evaluate the process performance to the continuous improvement of quality and productivity. Since the lifetime of products may possess a two-parameter exponential distribution, 14 estimators are used to estimate the lifetime performance index based on the multiply type II censored sample. These estimators are utilized to develop the new hypothesis testing algorithmic procedure in the condition of known L. Finally, two practical examples are illustrated to employ the testing algorithmic procedure to determine whether the process is capable.     

Uniformly most powerful unbiased test for shoulder condition in point transect sampling

Point transect sampling is a well-known methodology for estimating wildlife population density. In this context, the usual approach is to assume a model for the detection function. Thus, the estimate depends on the shape of the detection function. In particular, the estimation is influenced by the so-called shoulder condition, which guarantees that detection is nearly certain at small distances from the observer. For instance, the half-normal model satisfies this condition, whereas the negative exponential model does not. Testing whether the shoulder condition is consistent with data is a crucial issue. In this paper we propose the uniformly most powerful unbiased test for the shoulder condition in the exponential mixture model of the half-normal and the negative exponential. Critical values of the proposed test are calculated for large samples by means of asymptotic distribution theory and for small samples via Monte Carlo simulations. Finally, a case study is presented.     

Response-adaptive randomization for survival trials: the parametric approach

Summary.  Few references deal with response-adaptive randomization procedures for survival outcomes and those that do either dichotomize the outcomes or use a non-parametric approach. In this paper, the optimal allocation approach and a parametric response-adaptive randomization procedure are used under exponential and Weibull distributions. The optimal allocation proportions are derived for both distributions and the doubly adaptive biased coin design is applied to target the optimal allocations. The asymptotic variance of the procedure is obtained for the exponential distribution. The effect of intrinsic delay of survival outcomes is treated. These findings are based on rigorous theory but are also verified by simulation. It is shown that using a doubly adaptive biased coin design to target the optimal allocation proportion results in more patients being randomized to the better performing treatment without loss of power. We illustrate our procedure by redesigning a clinical trial.     

Effect of a new selection procedure on adaptive estimation

Adaptive estimation of parameters of some failure time distributionsis considered. A new procedure named the F-procedure has beendeveloped for selecting an appropriate model out of two possible models by Pandey et.al. (1991). Applying this F-procedure adaptive estimatorsof parameters of exponential, Wei bull, inverse Gaussian (IG) and Wald failure time distributions have been proposed in this paper. Comparison of these estimators has been undertaken with MLE's of the respective parameters and with some previous adaptiveestimators by simulation of samples using the Monte Carlo method.Adaptive estimation of parameters of some failure time distributions is considered. A new procedure named the F-procedure has been developedfor selecting an appropriate model out of two possible models by Pandey et.al. (1991). Applying this F-procedure adaptive estimators of parameters of exponential, Wei bull, inverse Gaussian (IG) and Wald failure time distributions have been proposed in this paper. Comparison of these estimators has been undertaken with MLE's of the respective parameters and with some previous adaptive estimators by simulation of samples using the Monte Carlo method.     

Minimax optimality of the Shiryayev–Roberts change-point detection rule

The result of Pollak [1985. Optimal detection of a change in distribution. Ann. Statist. 13, 206–227] proving the asymptotic optimality in sequential change-point detection of a suitable Shirayayev–Roberts stopping rule up to terms that vanish in the limit is generalized from the case of two completely specified distributions to that of a composite alternative hypothesis in a multidimensional exponential family. An explicit asymptotic lower bound on the expected Kullback–Leibler information required to detect a change-point is derived and is shown to be attained by a Shirayayev–Roberts stopping rule.     

Two stage fixed width confidence intervals for the common location parameter of several exponential distributins

Two stage sampling schemes are introduced for use in estimating the common location parameter (guarantee time) of two or more exponential distributions with a confidence interval of prespecified width whose coverage probability is at least a given nominal value. Exact expressions for all moments of order r ≥ 1 of the associated two stage sample sizes and for the actual coverage probabilities are derived. The performance of the procedures in a variety of two population, moderate fixed sample size cases is examined via numerical studies involving both exact calculations and Monte Carlo simulations. No new tables are needed to implement any of the proposed methods. A modified two stage procedure is recommended for practical use