Abstract: Suppose that an order restriction is imposed among several means in time series. We are interested in testing the homogeneity of these unknown means under this restriction. In the present paper, a test based on the isotonic regression is done for monotonic ordered means in time series with stationary process and short range dependent sequences errors. A test statistic is proposed using the penalized likelihood ratio (PLR) approach. Since the asymptotic null distribution of test statistic is complicated, its critical values are computed by using Monte Carlo simulation method for some values of sample sizes at different significance levels. The power study of our test statistic is provided which is more powerful than that of the test proposed by Brillinger (1989). Finally, to show the application of the proposed test, it is applied to real dataset contains monthly Iran rainfall records.
In this work, we introduce a new distribution for modeling the extreme values. Some important mathematical properties of the new model are derived. We assess the performance of the maximum likelihood method in terms of biases and mean squared errors by means of a simulation study. The new model is better than some other important competitive models in modeling the repair times data and the breaking stress data.
Abstract: In this paper the log-exponentiated-Weibull regression model is modified to allow the possibility that long term survivors are present in the data. The modification leads to a log-exponentiated-Weibull regression model with cure rate, encompassing as special cases the log-exponencial regression and log-Weibull regression models with cure rate typically used to model such data. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. Assuming censored data, we consider a classic analysis and Bayesian analysis for the parameters of the proposed model. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-exponentiated-Weibull error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.
Although the two-parameter Beta distribution is the standard distribution for
analyzing data in the unit interval, there are in the literature some useful and interesting alternatives which are often under-used. An example is the two parameter complementary Beta distribution, introduced by Jones (2002) and, to the best of our knowledge, used only by Iacobellis (2008) as a probabilistic model for the estimation of T year flow duration curves. In his paper the parameters of complementary Beta distribution were successfully estimated, perhaps due to its simplicity, by means of the L-moments method. The objective of this paper is to compare, using Monte Carlo simulations, the bias and mean-squared error, of the estimators obtained by the methods of L-moments and maximum likelihood. The simulation study showed that the maximum likelihood method has bias and mean -squared error lower than L-moments. It is also revealed that the parameters estimated by the maximum likelihood are negatively biased, while by the L-moments method the parameters are positively biased. Data on relative indices from annual temperature extremes (percentage of cool nights, percentage of warm nights, percentage of cool days and percentage of warm days) in Uruguay are used for illustrative purposes.
In this paper, a new four parameter zero truncated Poisson Frechet distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, residual and reversed residual life functions are investigated. The maximum likelihood method is used to estimate the model parameters. We assess the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling two real data sets to illustrate empirically its flexibility.