A two-parameter family of lifetime distribution which is derived from a model for static fatigue is presented. This derivation follows from considerations of the relationship between static fatigue crack extension and...
详细信息
A two-parameter family of lifetime distribution which is derived from a model for static fatigue is presented. This derivation follows from considerations of the relationship between static fatigue crack extension and the failure time of a certain specimen. The cumulative distribution function (cdf) of this new family is quite similar to the cdf of the half-normal distribution, and therefore this density is referred to as the generalized half-normal distribution (GHN). Furthermore, this GHN family is a special case of the three-parameter generalized gamma distribution. Even though the GHN distribution is a two-parameter distribution, the hazard rate function can form variety of shapes such as monotonically increasing, monotonically decreasing, and bathtub shapes. Some properties of this family are given, and examples are cited to compare with other commonly used failure time distributions such as Weibull, gamma, lognormal, and Birnbaum-Saunders.
This article concerns inference on the correlation coefficients of a multivariate normal distribution. Inferential procedures based on the concepts of generalized variables (GVs) and generalized p-values are proposed ...
详细信息
This article concerns inference on the correlation coefficients of a multivariate normal distribution. Inferential procedures based on the concepts of generalized variables (GVs) and generalized p-values are proposed for elements of a correlation matrix. For the simple correlation coefficient, the merits of the generalized confidence limits and other approximate methods are evaluated using a numerical study. The study indicates that the proposed generalized confidence limits are uniformly most accurate even for samples as small as three. The results are extended for comparing two independent correlations, overlapping and non-overlapping dependent correlations. For each problem, the properties of the GV approach and other asymptotic methods are evaluated using Monte Carlo simulation. The GV approach produces satisfactory results for all the problems considered. The methods are illustrated using a few practical examples. (c) 2006 Elsevier B.V. All rights reserved.
A common measure of the relative toxicity is the ratio of median lethal doses for responses estimated in two bioassays. Robertson and Preisler previously proposed a method for constructing a confidence interval for th...
详细信息
A common measure of the relative toxicity is the ratio of median lethal doses for responses estimated in two bioassays. Robertson and Preisler previously proposed a method for constructing a confidence interval for the ratio. The applicability of this technique in common experimental situations, especially those involving small samples, may be questionable because the sampling distribution of this ratio estimator may be highly skewed. To examine this possibility, we did a computer simulation experiment to evaluate the coverage properties of the Robertson and Preisler method. The simulation showed that the method provided confidence intervals that performed at the nominal confidence level for the range of responses often observed in pesticide bioassays. Results of this study provide empirical support for the continued use this technique.
A new two-parameter family of distribution is presented. It is derived to model the highly negatively skewed data with extreme observations. The new family of distribution is referred to as the logistic-sinh distribut...
详细信息
A new two-parameter family of distribution is presented. It is derived to model the highly negatively skewed data with extreme observations. The new family of distribution is referred to as the logistic-sinh distribution, as it is derived from the logistic distribution by appropriately replacing in exponential term with I hyperbolic sine term. The resulting family provides not only negatively skewed densities with thick tails but also variety of monotonic density shapes. The space of shape parameter, lambda greater than zero is divided by boundary line of lambda equals one, into two regions over which the hazard function is, respectively, increasing and bathtub shaped. The maximum likelihood parameter estimation techniques are discussed by providing approximate coverage probabilities for uncensored samples. The advantages of using the new family are demonstrated and compared by illustrating well known examples.
When prior information on model parameters is weak or lacking, Bayesian statistical analyses are typically performed with so-called "default" priors. We consider the problem of constructing default priors fo...
详细信息
When prior information on model parameters is weak or lacking, Bayesian statistical analyses are typically performed with so-called "default" priors. We consider the problem of constructing default priors for the parameters of survival models in the presence of censoring, using Jeffreys' rule. We compare these Jeffreys priors to the "uncensored" Jeffreys priors, obtained without considering censored observations, for the parameters of the exponential and log-normal models. The comparison is based on the frequentist coverage of the posterior Bayes intervals obtained from these prior distributions. (C) 2001 Elsevier Science B.V. All rights reserved.
We compare confidence intervals from a conditional procedure, the bootstrap, and the usual t-interval for a variety of symmetric and moderately skewed distributions. The simulations show superior performance of the co...
详细信息
We compare confidence intervals from a conditional procedure, the bootstrap, and the usual t-interval for a variety of symmetric and moderately skewed distributions. The simulations show superior performance of the conditional confidence intervals (CCI) and uniformly poor behavior for intervals based on the bootstrap for both symmetric and skewed distributions. Comparisons between the CCI, confidence intervals based on a 10% trimmed mean, and the CCI computed from a 10% trimming of the data show that the ''trimmed'' CCI produced shorter confidence intervals which maintain the nominal coverage probabilities better than either of the other two approaches for heavy-tailed, symmetric distributions. For skewed distributions, the usual CCI has better coverage than the t-interval, especially for small samples;however, the coverage of the CCI was still below the nominal level in many instances. The CCI, which can be calculated by inverting a permutation test, is easily calculated and is suitable for interactive use in most cases. SAS and S code for the CCI are available from the authors.
This paper discusses the problem of how large a sample to take from a population in order to make an inference about, or to take a decision concerning, some feature of the population. It first describes a fully Bayesi...
详细信息
This paper discusses the problem of how large a sample to take from a population in order to make an inference about, or to take a decision concerning, some feature of the population. It first describes a fully Bayesian treatment. It then compares this with other methods described in recent papers in The Statistician. The major contrast lies in the use of a utility function in the Bayesian approach, whereas other methods use constraints, such as fixing an error probability.
The bootstrap method is compared with the classical (linearization) and jackknife procedures for estimating the mean square errors (MSEs) of the ratio estimator and the combined ratio estimator. The initial samples ar...
详细信息
The bootstrap method is compared with the classical (linearization) and jackknife procedures for estimating the mean square errors (MSEs) of the ratio estimator and the combined ratio estimator. The initial samples are considered to be selected without replacement, and different procedures for selecting the bootstrap samples with or without replacement from them are examined. The biases, stabilities, coverage probabilities and confidence widths of all the procedures are compared.
If a priori information given by interval or ellipsoidal constraints on the unknown coefficients is used by (approximate) Minimax estimators, it is not ensured, that the estimates lie within the restricted set. In the...
详细信息
If a priori information given by interval or ellipsoidal constraints on the unknown coefficients is used by (approximate) Minimax estimators, it is not ensured, that the estimates lie within the restricted set. In the present paper, the probability of such events is investigated on the basis of multivariate two-sided normal probability integrals.
Simultaneous confidence interval procedures for multinomial proportions are used in many areas of science. In this article two new simultaneous confidence interval procedures are introduced. Numerical results are pres...
详细信息
Simultaneous confidence interval procedures for multinomial proportions are used in many areas of science. In this article two new simultaneous confidence interval procedures are introduced. Numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature. From the results presented in this article, it is evident that the new procedures are more accurate than the established ones, where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves. In the sample size determination problem, the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications. Because both procedures performed equally well, the procedure that requires the least amount of computing time is recommended.
暂无评论