The two parameter Gamma distribution is widely used for modeling lifetime distributions in reliability theory. There is much literature on the inference on the individual parameters of the Gamma distribution, namely the shape parameter k and the scale parameter theta when the other parameter is known. However, usually the reliability professionals have a major interest in making statistical inference about the mean lifetime mu, which equals the product thetak for the Gamma distribution. The problem of inference on the mean mu when both parameters theta and k are unknown has been less attended in the literature for the Gamma distribution. In this paper we review the existing methods for interval estimation of mu. A comparative study in this paper indicates that the existing methods are either too approximate and yield less reliable confidence intervals or are computationally quite complicated and need advanced computing facilities. We propose a new simple method for interval estimation of the Gamma mean and compare its performance with the existing methods. The comparative study showed that the newly proposed computationally simple optimum power normal approximation method works best even for small sample sizes.

We propose a simple close-to-normal approximation to a Weibull random variable (r.v.) and consider the problem of estimation of upper prediction limit (UPL) that includes at leastlout ofmfuture observations from a Weibull distribution at each ofrlocations, based on the proposed approximation and the well-known Box-Cox normal approximation. A comparative study based on Monte Carlo simulations revealed that the normal approximation-based UPLs for Weibull distribution outperform those based on the existing generalized variable (GV) approach. The normal approximation-based UPLs have markedly larger coverage probabilities than GV approach, particularly for small unknown shape parameter where the distribution is highly skewed, and for small sample sizes which are commonly encountered in industrial applications. Results are illustrated with a real dataset for practitioners.

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Almost every year, the Himalayan region suffers from a landslide disaster that is directly associated with the prosperity and development of the area. The study of landslide disasters helps planners, decision-makers and local communities for the development of anthropogenic structures in order to enhance the safety of society. Therefore, the prime aim of this research is to produce the landslide susceptibility map for the Chenab river valley using the bi-variate statistical information value model to detect and demarcate the areas of potential landslide incidence. The object-based image analysis method identified about 84 potential sites of landslides as landslide inventory. The statistical information value model is derived from the landslide inventory and multiple causative factors. The outcome showed that 23% area of the Chenab river valley falls into the class of a very high landslide susceptibility zone. The ROC curve method is used to validate the model which denoted the acceptable result for the landslide susceptibility zonation with 0.826 AUC value for the Chenab river valley.