A new log location-scale regression model with applications to voltage and Stanford heart transplant data sets is presented and studied. The martingale and modified deviance residuals to detect outliers and evaluate the model assumptions are defined. The new model can be very useful in analysing and modeling real data and provides more better fits than other regression models such as the log odd log-logistic generalized half-normal, the log beta generalized half-normal, the log generalized half-normal, the log-Topp-Leone odd log- logistic-Weibull and the log-Weibull models. Characterizations based on truncated moments as well as in terms of the reverse hazard function are presented. The maximum likelihood method is discussed to estimate the model parameters by means of a graphical Monte Carlo simulation study. The flexibility of the new model illustrated by means of four real data sets.
This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.
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.
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.