Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through th...Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through their medians. We calculate the confidence of the statement “the median of the first population is strictly smaller (larger) than the median of the second.” We analyze two real data sets and empirically demonstrate the quality of the confidence for such a statement. This confidence in the order of the medians is to be seen as a pre-analysis tool that can provide useful insights for comparing two or more populations. The method is entirely based on their exact distribution with no need for asymptotic considerations. We also provide the Quor statistical software, an R package that implements the ideas discussed in this work.展开更多
This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival...This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.展开更多
文摘Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through their medians. We calculate the confidence of the statement “the median of the first population is strictly smaller (larger) than the median of the second.” We analyze two real data sets and empirically demonstrate the quality of the confidence for such a statement. This confidence in the order of the medians is to be seen as a pre-analysis tool that can provide useful insights for comparing two or more populations. The method is entirely based on their exact distribution with no need for asymptotic considerations. We also provide the Quor statistical software, an R package that implements the ideas discussed in this work.
文摘This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.
