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In this paper, a new three-parameter lifetime distribution is introduced by combining an extended exponential distribution with a logarithmic distribution. This flexible distribution has increasing, decreasing and upside-down bathtub failure rate shapes. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by EM algorithm and their asymptotic variance and covariance are obtained. In order to assess the accuracy of the approximation of variance and covariance of the maximum likelihood estimator, a simulation study is presented to illustrate the properties of distribution.

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The analysis of spatio-temporal series is crucial but a challenge in different sciences. Accurate analyses of spatio-temporal series depend on how to measure their spatial and temporal relation simultaneously. In this article, one-sided dynamic principal components (ODPC) for spatio-temporal series are introduced and used to model the common structure of their relation. These principal components can be used in the data set, including many spatio-temporal series. In addition to spatial relations, trends, and seasonal trends, the dynamic principal components reflect other common temporal and spatial factors in spatio-temporal series. In order to evaluate the capability of one-sided dynamic principal components, they are used for clustering and forecasting in spatio-temporal series. Based on the precipitation time series in different stations of Golestan province, the efficiency of the principal components in the clustering of hydrometric stations is investigated. Moreover, forecasting for the SPI index, an essential indicator for detecting drought, is conducted based on the one-sided principal components.